Download - Options UG
-
8/10/2019 Options UG
1/234
CQG IntegratedClient Options UserGuideFebruary 22, 2013 | Version 14.1
-
8/10/2019 Options UG
2/234
2013 CQG Inc.
CQG, DOMTrader, SnapTrader, TFlow, and TFOBV are registered trademarks of CQG.
-
8/10/2019 Options UG
3/234
Table of Contents
About this Document .................................................................................................. 1
Whats New in this Version ....................................................................................... 2
Related Documents .................................................................................................. 2
Customer Support ................................................................................................... 2
Options in CQG .......................................................................................................... 3
Entering Options Symbols ......................................................................................... 4
Opening Options Applications .................................................................................... 5
CQG API and Options ............................................................................................... 6
Greeks and Volatility Definitions ................................................................................ 7
Standard Options Pricing Models ............................................................................... 9
Exotic Option Models.............................................................................................. 23
Interest-Rate Option Models ................................................................................... 32
Spread Options Model ............................................................................................ 41
Cumulative Normal Distribution Function Approximation ............................................. 46
Numerical Methods for Solving Equations ................................................................. 47
Numerical Differentiation ........................................................................................ 48
Trading Options..................................................................................................... 49
Setting Options Preferences ....................................................................................... 51
Setting Options Window View Preferences ................................................................ 53
Setting Options Calculator View Preferences ............................................................. 54
Setting Volatility Workshop View Preferences ............................................................ 55
Setting Strategy Analysis View Preferences............................................................... 57
Setting Volatility Preferences .................................................................................. 58
Setting Interest Rate Preferences ............................................................................ 60
Setting Price Filter Preferences ................................................................................ 61
Setting Greeks Scale Preferences ............................................................................ 62
Setting Advanced Preferences ................................................................................. 63
Setting Model Preferences ...................................................................................... 64
Setting Update Frequency Preferences ..................................................................... 65
Updating the Refresh Rate ...................................................................................... 66
Options Window ....................................................................................................... 67
Options Window Toolbar ......................................................................................... 72
Customizing Columns ............................................................................................. 75
-
8/10/2019 Options UG
4/234
Changing the Order of Columns ............................................................................... 78
Marking At-the-Money ............................................................................................ 79
Changing the Display Type ..................................................................................... 80
Opening Another Application from an Options Window ............................................... 81
Setting What If Options Parameters ......................................................................... 82
Copying Data to Excel ............................................................................................ 83
Placing Orders from the Options Window .................................................................. 84
Options Calculator .................................................................................................... 85
Options Calculator Components ............................................................................... 86
Options Calculator Toolbar ...................................................................................... 88
Using the Options Calculator ................................................................................... 90
Inputting What Ifs ................................................................................................. 92
Viewing Summary Statistics .................................................................................... 93
Using the Options Calculator Graph ......................................................................... 94
Using Cursors with an Options Calculator Graph ...................................................... 101
Information Displayed in an FX OTC View ............................................................... 102
Selecting the Properties for the Options Calculator Graph Lines ................................. 106
Options Graph ....................................................................................................... 107
Options Graph Toolbar ......................................................................................... 108
Define Options Graph Curves ................................................................................ 113
Volatility Workshop................................................................................................. 125
Volatility Workshop Components ........................................................................... 126
Volatility Workshop Toolbar .................................................................................. 129
Saving the Volatility Curve ................................................................................... 136
Opening a Saved Volatility Curve ........................................................................... 137
Adjusting the shape of the curve ........................................................................... 139
Removing Corrections .......................................................................................... 140
Selecting the Colors for the Volatility Workshop Graph Lines ..................................... 141
Designating the Approximation Characteristics ........................................................ 142
Modifying the Volatility Curve ................................................................................ 147
Resetting the Volatilities ....................................................................................... 148
Using 3D ............................................................................................................ 149
Strategy Analysis Window ....................................................................................... 153
Strategy Analysis Window Components .................................................................. 154
Strategy Analysis Toolbar ..................................................................................... 159
Selecting a Strategy ............................................................................................ 161
-
8/10/2019 Options UG
5/234
Selecting an Underlying Model for Strategy Displays ................................................ 164
Table Tabs .......................................................................................................... 171
Using the Display Tabs ......................................................................................... 187
Setting Properties for 3D Strategy Graph ................................................................ 191
Underlying Information ........................................................................................ 198
Display Properties................................................................................................ 199
Creating and Editing Strategies ............................................................................. 208
Saving an Options Strategy .................................................................................. 212
Loading a Saved Strategy ..................................................................................... 214
Using the Strategy Workspace Manager Window ..................................................... 215
Weights.............................................................................................................. 216
Using Advanced Strategy Features......................................................................... 221
Options Strategy Color Windows ........................................................................... 226
-
8/10/2019 Options UG
6/234
-
8/10/2019 Options UG
7/234
Page 1
Options User Guide
About this Document
This document is one of several user guides for CQG Integrated Client (CQG IC). This guidedetails options-specific tools in CQG.
You can navigate the document in several ways:
Click a bookmark listed on the left of the page.
Click an item in the Table of Contents.
Click a blue, underlined link that takes you to another section of the document. To goback, use Adobe Reader Page Navigation items (Viewmenu).
If you are looking for a particular term, it may be easier for you to search the document for it.
There are two ways to do that:
Right-click the page, and then click Find.
Press Ctrl+F on your keyboard.
This document is intended to be printed double-sided, so it includes blank pages before new
chapters.
Please note that images are examples only and are meant to demonstrate and expose system
behavior. They do not represent actual situations.
To ensure that you have the most recent copy of this guide, pleasego to the user guide page
on CQGs website.
http://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspx -
8/10/2019 Options UG
8/234
Page 2
About this Document
Whats New in this Version
Weve added a Costbutton and a multiplier button to theOptions Window toolbar.
Related Documents
CQG IC user guides:
CQG Basics
Charting and Studies
Advanced Analytics
TradingandCQG Spreader
Customer SupportCQG Customer Support can be reached by phone from Sunday, 2:30 p.m. CT through Friday,
5:00 p.m. CT. These hours also apply to Live Chat.
United States 1-800-525-1085
United Kingdom +44 (0) 20-7827-8270
France +33 (0) 1-74-18-07-81
Germany +49 (0) 69-6677-7558-0
Japan +81 (0) 3-3286-6877
Russia +7 495-795-2409
Singapore +65 6494-4911
Sydney +61 (2) 9235-2009
[email protected] hours a day, 7 days a week.
If you have questions about CQG documentation, pleasecontact the help author.
http://www.cqg.com/Docs/CQG_Basics_UG.pdfhttp://www.cqg.com/Docs/CQG_Basics_UG.pdfhttp://www.cqg.com/Docs/Charting_UG.pdfhttp://www.cqg.com/Docs/Charting_UG.pdfhttp://www.cqg.com/Docs/Analytics_UG.pdfhttp://www.cqg.com/Docs/Analytics_UG.pdfhttp://www.cqg.com/Docs/Trading_UG.pdfhttp://www.cqg.com/Docs/Trading_UG.pdfhttp://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfhttp://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfhttp://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfmailto:[email protected]:[email protected]:[email protected]:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfhttp://www.cqg.com/Docs/Trading_UG.pdfhttp://www.cqg.com/Docs/Analytics_UG.pdfhttp://www.cqg.com/Docs/Charting_UG.pdfhttp://www.cqg.com/Docs/CQG_Basics_UG.pdf -
8/10/2019 Options UG
9/234
Page 3
Options User Guide
Options in CQG
CQG IC includes five options applications:
Options Window
Options Calculator
Options Graph
Volatility Workshop
Strategy Analysis
All CQG IC users have access to the Options Window and the Options Graph. If you would liketo learn more about our advanced options offering, which includes Options Calculator, Options
Strategy, and Volatility Workshop,please contact CQG.
CQG offers seven basic option models that serve as the framework for valuing options: Black,
Black-Scholes, Bourtov, Cox-Ross-Rubinstein, Garman-Kohlhagen, Merton, and Whaley.
http://www.cqg.com/Support.aspxhttp://www.cqg.com/Support.aspxhttp://www.cqg.com/Support.aspxhttp://www.cqg.com/Support.aspx -
8/10/2019 Options UG
10/234
Page 4
Options in CQG
Entering Options Symbols
The format for options on futures is: C. for calls
and or P. for puts.
The strike price is 2-5 digits.
Example: C.SPZ081500 = December 2008 1500 call on the S&P 500 futures contract.
An alternate format is C._. for calls and with P.for puts.
C.SP_U8.1500 = September 2008 1500 call on the S&P 500 futures contract.
On Options windows, you can enter the symbol only.
For at the money for the nearby month, type C. or P., the symbol, and ?.
For at the money for some other month, type C.orP., the symbol, the month, the year, and ?
and then press CTRL+ENTER.
For strikes for the most active month, type C.or P.and the symbol and ?and then pressCTRL+ENTER.
-
8/10/2019 Options UG
11/234
Page 5
Options User Guide
Opening Options Applications
Click the Optionsbutton on the main toolbar, and then click the name of the options window
you want to open:
This button provides access to all options windows without having to display the button for each
window.
If the Optionsbutton is not displayed, click the Morebutton, and then click Options.
You can also add individual options windows to the toolbar:
-
8/10/2019 Options UG
12/234
Page 6
Options in CQG
CQG API and Options
CQGs API supports efficient access to options strike properties through the use of the
CQGInstrumentsGroup interface.
With one request to CQG servers, your application can subscribe to all strikes in any givencontract month or a range of months.
Data subscription levels can also be configured to optimize instrument resolution for strikeproperties and market data, allowing for the delivery of critical information without unnecessary
overhead.
CQG also offers access to common real-time values for all subscribed options strikes: Greeks,
theoretical values and implied volatilities.
Through the API, CQG offers in-depth portfolio analysis capabilities.
-
8/10/2019 Options UG
13/234
Page 7
Options User Guide
Greeks and Volatility Definitions
As you work with options in CQG IC, its helpful to understand how implied and average
volatility are calculated and how the Greeks are defined.
Delta
Delta shows the change in the price of a derivative to the change in the price of the underlyingassets. Sometimes delta is known as the hedge ratio, as delta indicates how much of theunderlying asset needs to be bought or sold to hedge the option. Traders take advantage of
delta by creating delta hedging, delta spreads, and delta neutral.
Delta values are positive numbers less than or equal to 100. They represent the ratio of thechange in the theoretical value over the change in the underlying price.
Values:
Out of the money = close to 0
At the money = close to +0.5
In the money = close to +1
Calls = positive
Puts = negative
Delta values for the out-of-the-money series move closer to 0 as expiration nears. Likewise,
more in-the-money options have deltas close to 1 as expiration approaches.
For example: If the underlying S&P 500 contract stands at 134020, with a delta of 52.73, and a
theoretical value of 2600.5, and the underlying price increases to 134220, while the delta risesto 54.02, the theoretical value increases to 2707.
The calculations are:
134220 134020 = 200
(52.73 + 54.02)/2 = 106.750
53.375 *2 = 106.750
The deltas from one underlying price to the next are interpolated.
106.750 + 2600.5 = 2707.25 new theoretical value
Gamma
Gamma is the amount the delta changes when the underlying price changes by one tick.
Gamma is greatest for at-the-money options. Gamma increases as the option moves closer to
expiration. Traders try to limit gamma risk because short gamma positions create a potentialfor losses.
For example: If the delta of an S&P future was 91.80, the gamma was .01 and the price of an
S&P future increased from 1340.80 to 1340.90 i.e., a one-tick increase, the delta wouldincrease to 91.81.
-
8/10/2019 Options UG
14/234
Page 8
Options in CQG
Theta
Theta represents the loss in theoretical value in one day, if all other factors are constant. Inother words, it attempts to isolate the time decay factor.
For example: Assume the amount showing the Value column was 2725.1, with 15 days until
expiration and a theta value of 92.053. You would expect to see the amount in the Valuecolumn decrease approximately 92 dollars the following day. A more precise definition of the
amount of the time value lost is an average of the Thetas on the dates under consideration. So,if the theta on the following day was 95.201, the decrease in theoretical value would be:
(92.053 + 95.201)/2 = 93.6
Vega
Vega is the amount that the theoretical value changes when the volatility changes by 1 point.
For example: Assume a June Corn contract had a vega of 1.421, a volatility of 25.90, and atheoretical value of 45.4. If the volatility were to increase to 26.90, the vega says that the
theoretical value would increase by 1.4 dollars to 46.8, provided the other factors affectingoptions prices remained constant.
The display also indicates the days until expiration, as well as the volatility and interest rate
assumptions underlying the data.
Rho
Rho is the change in option price to a unit change in interest rates. When the interest rateincreases, the call option price increases also and put option price falls.
For example: Assume the starting call value is 4.2012, the interest rate r is 5% and zero-coupon rate b is 2%. Rho(r)(per 1%)= 0.1243, and Rho(b)(per 1%)=0.1328, If r rises to 6%
and b stays at 5%, the call value is 4.3255. If r stays at 5% and b rises to 3%, the call value is4.334.
Implied Volatility
The implied volatility calculated from an options display represents the volatility that, if entered
into a theoretical pricing model, would produce a theoretical value equal to the market price of
the option. Unlike the Historical Volatility study, the Implied Volatility calculation depends onthe model selected, the calculation method chosen and the parameters input in the What if?
column.
Average Volatility
The average volatility is calculated using the following formula:
( ) ( )( )LH
LHHL
SPSP
SPUPIVUPSPIVAvgV
+=
-
8/10/2019 Options UG
15/234
Page 9
Options User Guide
Standard Options Pricing Models
Options pricing models describe mathematically how a set of input parameters typically
underlying price, strike price, time to expiration, interest rate, and volatility combine to
determine a theoretical value of an option.CQG offers seven basic option models that serve as the framework for valuing options: Black,
Black-Scholes, Bourtov, Cox-Ross-Rubinstein, Garman-Kohlhagen, Merton, and Whaley.
Term Definition
TheoV option theoretic value
sigma, volatility of the relative price change of the underlying stock price
ImpV implied volatility
Greeks Partial derivatives of the option price to a small movement in the underlying
variables. Main greeks are delta, gamma, theta, vega, rho.
Delta, delta is the first derivative of the option price by underlying price
Gamma, gamma is the second derivative of the option price by underlying price
Vega vega is the first derivative of the option price by volatility
Theta, theta is the first derivative of the option price by time to expiration
Rho, rho is the first derivative of the option price by interest rate
N(x) the cumulative normal distribution function
n(x) normal distribution function
,
S underlying price
X strike price of option
r risk-free interest rate
T option time to expiration in years
=
x z
dzexN 22
2
1)(
2
2
2
1)(
x
exn
=
2
2
2
1)(
x
exxn
=
-
8/10/2019 Options UG
16/234
Page 10
Options in CQG
Term Definition
volatility of the relative price change of the underlying instrument
b the cost-of-carry rate of holding the underlying security
For further reading, we suggest:
The Complete Guide to Option Pricing Formulas. ISBN 0071389970.
Options, Futures, and Other Derivatives. ISBN 0132164949.
Option Volatility and Pricing Strategies. ISBN155738486X.
-
8/10/2019 Options UG
17/234
Page 11
Options User Guide
Black Model
In 1976, Fisher Black developed a modification to the Black-Scholes model designed to price
options on futures more precisely. The model assumes that futures can be treated the sameway as securities, providing a continuous dividend yield equal to the risk-free interest rate.
The model provides a good correction to the original model concerning options on futures.
However, it still carries the restrictions of the Black-Scholes evaluation.
Notation
Theoretical value of a call
Theoretical value of a put
Underlying price
Strike price
Interest rate
Time to expiration in years
Volatility
Cumulative normal density function
The theoretical values for calls and puts are:
Where:
Note: Although similar, this definition of is different from the one used in the Black-Scholesmodel.
An alternative form for is:
C
P
U
E
r
t
)(xN
)()( thNEehNUeC rtrt =
)()( htNEehNUeP rtrt +=
2
)/ln( t
t
EUh
+=
h
h
t
tEUh
2
)/ln(2 2+=
-
8/10/2019 Options UG
18/234
Page 12
Options in CQG
Generalized Black-Scholes (Black-Scholes extended) Model
The generalized Black-Scholes model can be used to price European options on stocks without
dividends [Black and Scholes (1973) model], stocks paying a continuous dividend yield [Merton(1973) model], options on futures [Black (1976) model], and currency options [Garman and
Kohlhagen (1983) model].
TheoV
Call
Put
where
N(x) the cumulative normal distribution function;
S underlying price;
X strike price of option;
r risk-free interest rate;
T time to expiration in years;
volatility of the relative price change of the underlying stock price.
b the cost-of-carry rate of holding the underlying security.
b = r gives the Black and Scholes (1973) stock option model.
b = r q gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 gives the Black (1976) futures option model.
b = r rf gives the Garman and Kohlhangen (1983) currency option model (rf- risk-free
rate of the foreign currency).
Delta
Call
Put
)()(C 21)(
GBS dNeXdNeSc TrTrb ==
)()(P 1)(
2GBS dNeSdNeXp TrbTr ==
( )T
TbXSd
++=
2/)/ln( 2
1
Tdd = 12
)( 1)(
dNe Trb=
[ ]1)( 1)( = dNe Trb
-
8/10/2019 Options UG
19/234
Page 13
Options User Guide
Gamma
Gamma is identical for put and call options.
where
- normal distribution function.
Vega
Vega is identical for put and call options.
Theta
Call
Put
Rho
Call
where
c call TheoV
Put
where
p put TheoV
TS
edn Trb
=
)(
1)(
2
2
2
1)(
x
exn
=
TdneSVega Trb = )( 1
)(
)()()(2
)(21
)(1
)(
dNXrdNeSrbT
dneS rTTrbTrb
++
=
)()()(2
)(21
)(1
)(
dNXrdNeSrbT
dneS rTTrbTrb
=
=
=
0
0),( 2
bwhencT
bwhendNeXT rT
=
=
0
0),( 2
bwhenpT
bwhendNeXT rT
-
8/10/2019 Options UG
20/234
Page 14
Options in CQG
Implied volatility
To find implied volatility the following equations should be solved for the value of sigma:
Call
Put
where
This equation has no closed form solution, which means the equation must be numerically
solved to find .
Bourtovs Model
Bourtovs model is based on the Black-Scholes model. It defines a special method to calculatevolatility, which is an input parameter of the Pricing Model Calculator.
)()( 21)(
dNeXdNeSc TrTrb =
)()( 1)(
2 dNeSdNeXp TrbTr =
( )T
TbXSd
+=
2/)/ln( 2
1
Tdd = 12
-
8/10/2019 Options UG
21/234
Page 15
Options User Guide
Cox-Ross-Rubinstein Model
The Cox-Ross-Rubinstein binomial model can be used to price European and American options
on stocks without dividends, stocks and stock indexes paying a continuous dividend yield,futures, and currency options.
TheoV
The main binomial model assumption is the underlying price can either increase by a fixed
amount uwith probabilityp, or decrease by a fixed amount dwith probability 1-p. So the
underlying price at each node is set equal to
where
S underlying price;
u, d up and down jump sizes that underlying price can take at each time step.
Option pricing is done by working backwards, starting at the terminal date. Here we know allthe possible values of the underlying price. For each of these, we calculate the payoffs from the
derivative, and find what the set of possible derivative prices is one period before. Given these,
we can find the option one period before this again, and so on. Working ones way down to theroot of the tree, the option price is found as the derivative price in the first node.
Call
At expiration date:
where n number of time steps.
At each previous step:
European exercise
American exercise
where
price up movement size;
price down movement size;
size of each time step;
up movement probability;
b the cost-of-carry, defined as:
b = r to price European and American options on stocks;
jiduS iji ,...,1,0, =
niXduSf inini ,...,1,0),0,max(, ==
[ ]1,1,1, )1( +++ += jijitrji fpfpef
[ ]( )1,1,1, )1(,max +++ += jijitrijiji fpfpeXduSf
= teu
== ued t /1
nTt /=
=
du
dep
tb
-
8/10/2019 Options UG
22/234
Page 16
Options in CQG
b = r q to price European and American options on stocks and stock indexes paying acontinuous dividend yield q;
b = 0 to price European and American options on futures;
b = r rf to price European and American currency options (rf risk-free rate of theforeign currency).
Put
At expiration date:
At each previous step:
European exercise
American exercise
Delta
Given the values calculated for the price, Delta approximation is
Gamma
Gamma approximation is
Theta
Theta can be approximated as
Vega, Rho
System uses the numerical differentiation to calculate the Greeks.
Implied volatility
System numerically finds implied volatility.
niduSXp inini ,...,1,0),0,max(, ==
[ ]1,1,1, )1( +++ += jijitrji fpfpef
1,1,1, )1(,max +++
+= jiji
triji
ji fpfpeduSXf
jif ,
dSuS
ff
S
f
=
= 0,11,1
( ) ( )( )22
2
0,21,2
2
1,22,2
2
2
5.0 dSuS
dSduSffduSuSff
S
f
=
=
t
ff
=
2
0,00,2
-
8/10/2019 Options UG
23/234
Page 17
Options User Guide
Garman-Kohlhagen Model
This model, developed to evaluate currency options, considers foreign currencies analogous to a
stock providing a known dividend yield. The owner of foreign currency receives a dividendyield equal to the risk-free interest rate available in that foreign currency. The model assumes
price follows the same stochastic process presumed in the Black-Scholes model.
This model is used to evaluate options written on currencies. The interest rate of the nativecurrency is used as the default, but you can set the foreign interest rate inModel preferences.
This model corrects the difference between native and foreign interest rates. However, as a
modification of Black-Scholes model, it possesses all its limitations.
Notation
Theoretical value of a call
Theoretical value of a put
Underlying price
Strike price
Interest rate
Interest rate in the foreign country
Time to expiration in years
Volatility
The European call price is given by:
Where:
The Europeanput price is given by:
C
P
U
E
r
fr
t
)()( thNEehNUeC rttr
=
t
trrEUh
f
)2/()/ln( 2++=
)()( htNEehNUeP rttrf +=
-
8/10/2019 Options UG
24/234
Page 18
Options in CQG
Merton Model
In 1973, Merton produced a model with a non-constant interest rate. He assumed that interest
rates follow a special type of random process.
By taking into consideration the dynamic process of interest rate determination, and thecorrelation between the underlying price and the options price, this model provides an
improvement over the Black-Scholes model. This model is generally used to value Europeanoptions written on stocks.
Notation
Theoretical value of a call
Theoretical value of a put
Underlying price
Strike price
Time to expiration in yearsCumulative normal density function
Volatility
Volatility of an interest rate contract
Interest rate
Correlation between the underlying and interest rate contracts
The theoretical values for European calls and puts are:
Where:
C
P
U
E
t)(xN
p
)(tR
)()()( thENtBhUNC =
)()()( htENtBhUNP +=
t
ttBXUh
2/)()(ln)/ln( +=
+=t
pp dtt0
22 )2()(
ttRetB
)()( =
-
8/10/2019 Options UG
25/234
Page 19
Options User Guide
Whaley Model
The quadratic approximation method by Baron-Adesi and Whaley (1987) can be used to price
American options.
TheoV
Call
where
b the cost-of-carry rate;
b = r to price options on stocks.b = r q to price options on stocks and stock indexes paying a continuous dividend yield q
b = 0 to price options on futures.
b = r rf to price currency options (rf risk-free rate of the foreign currency).
CGBS the generalized Black-Scholes call TheoV expression;
S* the critical commodity price for the call option that satisfies
The last equation should be numerically solved to find S*.
Put
+=
**
****
11)/(),,,,,(
SSwhenSX
SSwhenSSAbrTXSPp
q
GBS
-
8/10/2019 Options UG
26/234
Page 20
Options in CQG
where
PGBS the generalized Black-Scholes put TheoV expression;
S** the critical commodity price for the put option that satisfies
The last equation should be numerically solved to find S**.
Delta
Call
where
GBS- the generalized Black-Scholes call expression.
Put
where
GBS- the generalized Black-Scholes put expression.
( )[ ])(1 **1)(1
**
1 SdNeq
SA
Trb =
2
/4)1()1( 2
1
KMNNq
+=
( )[ ])(1),,,,,( **1)(1
****** SdNe
q
SbrTXSPSX TrbGBS =
+=
**
****1
11
1
)/(),,,,,( 11
SSwhen
SSwhenSSqAbrTXS qq
GBS
-
8/10/2019 Options UG
27/234
Page 21
Options User Guide
Gamma
Call
Put
Vega
Call
Put
Theta
Call
where
GBS- the generalized Black-Scholes call expression.
Put
where
GBS- the generalized Black-Scholes put expression.
+=
**
****2
111
0
)/()1(),,,,,( 11
SSwhen
SSwhenSSqqAbrTXS qq
GBS
=
**
**
0 SSwhen
SSwhenationdifferentiNumericalVega
= **
**
0 SSwhenSSwhenationdifferentiNumerical
-
8/10/2019 Options UG
28/234
Page 22
Options in CQG
Rho
Call
where
GBS- the generalized Black-Scholes call expression.
Put
where
GBS- the generalized Black-Scholes put expression.
Implied volatility
System numerically finds implied volatility.
Implied volatility cant be calculated for call option if option value is less than (underlying price
- strike).
Implied volatility cant be calculated for put option if option value is less than (strike -
underlying).
=
**
**
0 SSwhen
SSwhenationdifferentiNumerical
-
8/10/2019 Options UG
29/234
Page 23
Options User Guide
Exotic Option Models
For further reading, we suggest:
The Complete Guide to Option Pricing Formulas. ISBN 0071389970.
Barrier Options,Binary/Digital Options,andLookback Optionsat www.global-derivatives.com.
Standard (Vanilla) Barrier
There are two kinds of the barrier options:
In = Paid for today but first come into existence if the underlying price hits the barrier Hbefore expiration.
Out = Similar to standard options except that the option is knocked out or becomesworthless if the underlying price hits the barrier before expiration.
TheoV
In Barriers
Down-and-in call
c(X>=H) = C + E = 1, = 1
c(X=H) = A + E = -1, = 1
c(X=H) = B C + D + E = 1, = -1
p(X=H) = A B + D + E = -1, = -1
p(X=H) = A C + F = 1, = 1
c(X
-
8/10/2019 Options UG
30/234
Page 24
Options in CQG
Up-and-out call
c(X>=H) = F = -1, = 1
c(X=H) = A B + C D + F = 1, = -1
p(X=H) = B D + F = -1, = -1
p(X
-
8/10/2019 Options UG
31/234
Page 25
Options User Guide
K possible cash rebate,
b the cost-of-carry.
b = r to price options on stocks.
b = r q to price options on stocks and stock indexes paying a continuous dividend yield q
b = 0 to price options on futures.
b = r rf to price currency options (rf risk-free rate of the foreign currency).
Delta, Gamma, Vega, Theta, Rho
The system uses the numerical differentiation to calculate the Greeks.
Implied volatility
The software shall numerically find implied volatility.
2
2 2
r+=
-
8/10/2019 Options UG
32/234
Page 26
Options in CQG
Asset-or-Nothing Binary
At expiry, the asset-or-nothing call option pays 0 if S X. Similarly, a put
option pays 0 if S >=X and S if S < X.
TheoV
Call
Put
where
b the cost-of-carry.
b = r to price options on stocks.
b = r q to price options on stocks and stock indexes paying a continuous dividend yield q
b = 0 to price options on futures.
b = r rf to price currency options (rf risk-free rate of the foreign currency).
Delta
Gamma
)()( dNeSc Trb =
)()( dNeSp Trb =
2
ln( / )
2
S X b T
dT
+ +
=
( )
( )
( )( ( ) )
( )( ( ) )
b r T
call
b r T
put
n de N d
T
n de N d
T
= +
=
( )
( )
( )(1 )
( )(1 )
b r T
call
b r T
put
de n d
T
S Td
e n dT
S T
=
=
-
8/10/2019 Options UG
33/234
Page 27
Options User Guide
Vega
Theta
Rho
Implied volatility
To find implied volatility the following equations should be solved for the value of sigma:
Call
Put
System numerically solves these equations.
( )
2
( )
2
ln( / )( )
2
ln( / )( )
2
b r T
call
b r T
put
T S X bT V Se n d
T
T S X bT V Se n d
T
+=
+=
( )
++
+=
2
/ln
2
)()()(
2)(
b
T
XS
T
dndNrbeS Trbcall
( )
++
=
2
/ln
2
)()()(
2)(
b
T
XS
T
dndNrbeS Trbput
( )
( )
( )0
( )0
( ) 0
( ) 0
b r T
call
b r T
put
rT
call
rT
put
Se n d T b
T
Se n d T b
T
STe N d b
STe N d b
=
=
= =
= =
)()( dNeSc Trb =
)()( dNeSp Trb =
-
8/10/2019 Options UG
34/234
Page 28
Options in CQG
Floating Strike Lookback
The Lookback models are used to price European lookback options on stocks without dividends,
stocks and stock indexes paying a continuous dividend yield and currency options.
A floating strike lookback call gives the holder of the option the right to buy the underlyingsecurity at the lowest price observed, Smin, in the life of the option. Similarly, a floating strike
lookback put gives the option holder the right to sell the underlying security at the highest priceobserved, Smax, in the options lifetime.
TheoV
Call
where
b the cost-of-carry;
b = r to price options on stocks;
b = r q to price options on stocks and stock indexes paying a continuous dividend yield
q;
b = r rf to price currency options (rf risk-free rate of the foreign currency);
Put
where
.
+
+=
)(2
2)()( 11
2
min
2
2min1
)(
2
aNeTb
aNS
S
beSaNeSaNeSc bT
b
rTrTTrb
T
TbSSa
++=
)2/()/ln( 2min
1
Taa = 12
+
+=
)(2
2)()( 11
2
max
2
1
)(
2max
2
bNeTb
bNS
S
beSbNeSbNeSp bT
b
rTTrbrT
T
TbSSb
++=
)2/()/ln( 2max1
Tbb = 12
-
8/10/2019 Options UG
35/234
Page 29
Options User Guide
Delta, Gamma, Vega, Theta, Rho
The system uses the numerical differentiation to calculate the Greeks.
Implied volatility
The system uses numerically find implied volatility.
-
8/10/2019 Options UG
36/234
Page 30
Options in CQG
Fixed Strike Lookback
In a fixed strike lookback call, the strike is fixed in advance, and at expiry the option pays out
the maximum of the difference between the highest observed price, Smax, in the optionlifetime and the strike X, and 0. Similarly, a put at expiry pays out the maximum observed
price, Smin, and 0.
TheoV
Call
when X > Smax
where
b the cost-of-carry;
b = r to price options on stocks;
b = r q to price options on stocks and stock indexes paying a continuous dividend yieldq;
b = r rf to price currency options (rf risk-free rate of the foreign currency);
when X =Smin
+
+=
)(2
2)()( 11
22
21
)(2
dNeTb
dNX
S
beSdNeXdNeSc
bT
b
rTrTTrb
T
TbXSd
++=
)2/()/ln( 2
1
Tdd = 12
+
++=
)(2
2)()()( 11
2
max
2
2max1
)(
max
2
eNeTb
eNS
S
beSeNeSeNeSXSec
bT
b
rTrTTrbrT
T
TbSSe
++=
)2/()/ln( 2max1
Tee = 12
+
+=
)(2
2)()(
11
22
1
)(
2
2
dNeTb
dNX
S
beSdNeSdNeXp bT
b
rTTrbrT
-
8/10/2019 Options UG
37/234
Page 31
Options User Guide
where
By defining the following variables all four formulas can be combined into one:
- option type adjustment,
Now the formulas transform into:
Delta, Gamma, Vega, Theta, Rho
The system uses the numerical differentiation to calculate the Greeks.
Implied volatility
The systems finds implied volatility numerically.
+
++=
)(2
2)()()( 11
2
max
2
2min1
)(
min
2
fNeTb
fNS
S
beSfNeSfNeSSXep
bT
b
rTrTTrbrT
T
TbSSf
++=
)2/()/ln( 2
min1
Tff = 12
z
=
optionput1
,optioncall1z
observed,extremepriceS
=option;putagcalculatinif,
option,callagcalculatinif
min
max,
S
SS
,limitpriceLS
=otherwise;,
puts,fororcallsforif,
X
XSXSSSL
( )
+=
=
+
+
++=
TbdN(zS/S)dN(ze
b
S)dN(zSXSez
)dN(zeT
bdzN
S
S
b
eSz
)dN(zeSz)dN(zeSzX)(SezTheoV
b
L
bT
LL
rT
bT
b
rT
rTr)T(b
L
rT
L
2
2
2
2
1
2
1
2
2
11
2
max
2
21
2
2
-
8/10/2019 Options UG
38/234
Page 32
Options in CQG
Interest-Rate Option Models
For further reading, we suggest The Complete Guide to Option Pricing Formulas. ISBN
0071389970.
The Vasicek Model
The Vasicek (1977) model is a yield-based one-factor equilibrium model. The model allowsclosed-form solutions for European options on zero-coupon bonds.
TheoV
Call
Put
where
L bond principal (i.e. face value),
bond time to maturity,
,
,
P(T)-the price at time zero of a zero-coupon bond that pays $1 at time T,
wherer the initial risk-free rate
)()( pT hNPXhNPLc =
)()( hNPLhNPXp pT +=
)(TPPT=
)(
PP =
2ln
1 p
Tp XP
PLh
+
=
dp =
( ) ( )a
ee
ad
aTTa
2
11
1 2)(
=
rTBeTATP
= )()()(
a
eTB
aT=
1)(
( )( )
=
a
TB
a
baTTBTA
4
)(2/)(exp)(
22
2
22
-
8/10/2019 Options UG
39/234
-
8/10/2019 Options UG
40/234
Page 34
Options in CQG
Call
Put
Implied volatility
System numerically finds implied volatility.
( ) ( ) ( ) ( )p
TpTpTT
p
T
T
BBhnPXhNBPXhNBPL
BBhnPL
r
c
+
=
=
( ) ( ) ( ) ( ) pT
pTpTTp
T BB
hnPXhNBPX
BB
hnPLhNBPLr
p
+
+=
=
-
8/10/2019 Options UG
41/234
Page 35
Options User Guide
The Hull and White Model
The Hull and White (1990) model is a yield-based no-arbitrage model. This is extension of the
Vasicek model. The model allows closed-form solutions for European options on zero-couponbonds.
TheoV
Call
Put
Where
L bond principal (i.e. face value),
bond time maturity,
,
,
P(T) - the price at time zero of a zero-coupon bond that pays $1 at time T,
a the speed of the mean reversion.
Unlike Vasicek model, PTand Pare input parameters.
Delta
Call
Put
)()( pT hNPXhNPLc =
)()( hNPLhNPXp pT +=
)(TPPT=
)(
PP =
2)(
)(ln
1 p
p XTP
PLh
+
=
( ) ( )aeea
aT
Tap
211
2
)(
=
( ) ( ) ( )TppppT P
hnPLhNXhnXP
c
=
=
11
( ) ( ) ( )Tp
p
p
p
T PhnPLhNXhnX
P
p
++=
=
11
-
8/10/2019 Options UG
42/234
Page 36
Options in CQG
Gamma
Gamma is identical for put and call options.
Vega
Because
Theta
Call
Put
where
( ) ( )Tp
p
pTpT P
hhnX
h
P
hnPL
P 22
11
+
=
=
( ) ( )xnxn =
( ) ( )
hhnPX
hhnPL
pcVega pT
p +
=
=
=
+
+
+
+=
=
p
ppTpT
p
p
rghnPXhNPrX
rghnPL
T
c
'
2
1)()('
2
1)(
=
XP
PLg
Tp
ln
12
( )TPT
r ln1
=
+
++
+
++=
=
p
p
p
ppTpT
rghnPL
rghnPXhNPrX
T
p
'
2
1)('
2
1)()(
( ) ( )( )
+
=
aT
TaaTaTTa
p
ea
ee
a
ee
2
)(22)(
12
1
2
1'
-
8/10/2019 Options UG
43/234
Page 37
Options User Guide
Rho
Since, the price at time zero of a zero-coupon bond that pays $1 at time t is
then
Call
Put
Implied volatility
The system finds implied volatility numerically.
rtetP
=)(
TT PTP =
PP =
p
Th
=
( ) ( ) ( ) ( )p
pTpT
pT
ThnPXhNTPXhNPL
ThnPL
r
c
+
=
=
( ) ( ) ( ) ( )p
pTpT
p
ThnPXhNTPX
ThnPLhNPL
r
p
+
+=
=
-
8/10/2019 Options UG
44/234
Page 38
Options in CQG
The Ho and Lee Model
Ho and Lee (1986) model is the no-arbitrage model. The model allows closed-form solutions for
European options on zero-coupon bonds.
TheoV
Call
Put
Where
L bond principal (i.e. face value),
bond time maturity,
,
,
P(T) - the price at time zero of a zero-coupon bond that pays $1 at time T,
The distinctions from Vasicek model are
- PTand Pare input parameters,
- pexpression is different.
Delta
Call
Put
)()( pT hNPXhNPLc =
)()( hNPLhNPXp pT +=
)(TPPT=
)(
PP =
2)(
)(ln
1 p
p XTP
PLh
+
=
( ) TTp =
( ) ( ) ( )Tp
p
p
p
T PhnPLhNXhnX
P
c
=
=
11
( ) ( )2 21
1 pT p T p p T
h hL P n h X n h
P P P
= = +
-
8/10/2019 Options UG
45/234
Page 39
Options User Guide
Gamma
Gamma is identical for put and call options.
Vega
Because
Theta
Call
Put
where
,
( ) ( )
+
+=
=
pTp
p
pTpT P
hnX
P
hnPL
P
11
111
12
( ) ( )xnxn =
( ) ( )
hhnPX
hhnPL
pcVega pT
p +
=
=
=
+
+
+
+=
=
p
ppT
pT
p
p
rghnPX
hNPrXr
ghnPLT
c
'2
1)(
)('2
1)(
=
XP
PLg
Tp
ln
12
( )TPT
r ln1=
++++=
=
p
p
p
ppTpT
rghnPL
rghnPXhNPrX
T
p
'2
1)(
'2
1)()(
[ ]TT
p 32
' =
-
8/10/2019 Options UG
46/234
Page 40
Options in CQG
Rho
Since the price at time zero of a zero-coupon bond that pays $1 at time t is
then
Call
Put
Implied volatility
The system finds implied volatility numerically.
rtetP
=)(
TT PTP =
PP =
p
Th
=
( ) ( ) ( ) ( )p
pTpT
pT
ThnPXhNTPXhNPL
ThnPL
r
c
+
=
=
( ) ( ) ( ) ( )p
pTpT
p
ThnPXhNTPX
ThnPLhNPL
r
p
+
+=
=
-
8/10/2019 Options UG
47/234
-
8/10/2019 Options UG
48/234
Page 42
Options in CQG
, and is calculated by the formula above than may be expressed as
,
which is exactly identical to BS equation. Similar is true for . That also implies that some of
Greeks can be calculated by the corresponding BS formulas.
Prior to giving formulas for Greeks lets introduce a few helper equations which may help inimplementing the formulas found across the section.
, thus simplifying .
Put-call parity in Kirks model is expressed as:
.
Below are some partial derivatives used in equations
.
The first derivative of sigma by the price of the second futures is:
.
The second derivative of sigma by the price of the second futures is a bit more complex and is:
.
Partial derivatives of by the price of the second futures are also useful to have. Those are:
,
.
Also, some partial derivatives of the combined volatility are as follow:
,
,
c
)()( 21 dNXedNSecc TrTr
BS
==
p
=XF
F
+
2
22
122
1 2+=
( )12 FXFecp rT ++=
( ) 111
2
1
1
=
=
TF
F
d
F
d
( )22
12
2 XF
X
F +
=
( )
( ) ( )
+++
+
+
=
2
21
2
2
3
2
2
2
2
2
2
2
F
XF
XF
X
XF
X
F
21,dd
( )XFTd
FF
d
+
=
2
2
22
1 11
( )XFTd
FF
d
+
=
2
1
22
2 11
= 1
1
=
2
1
2
-
8/10/2019 Options UG
49/234
Page 43
Options User Guide
.
Finally it should be noted that
,
and hence:
.
Delta1, Delta2
Each delta is calculated with respect to the corresponding asset price movement. Sensitivity of
call option price to price change of the first futures is:
.
Sensitivity of call option price to price change of the second futures is:
.
By virtue of call-put parity given above the following expressions are true for put option Deltas.Sensitivities of put option price to price change in price of either the first or the second futures
are, respectively:
,
.
Gamma1, Gamma2
Each gamma is calculated similar to delta, with respect to the corresponding asset pricemovement.
The equation is identical for call and put:
The gamma with respect to the second futures price is identical for call and put and isexpressed as:
.
1=
0/)()( 21 = Fdndn
)()( 21 dndnF =
( )11
1 dNeF
c rTc =
=
( ) ( )
++=
=
2
222
2
2 )(F
TdnXFdNeF
c rTc
rTcp eF
p =
=
11
1
rTcp eF
p +=
= 2
2
2
( )[ ] ( )[ ] ( )TFdnedTdn
FdTdn
TFe rTrTpc
1
122112
1
11 11 =
++==
( ) ( )
++
+
==
22
222
2
2
2
22
2222
FF
dd
FXF
FT
F
ddne
rTpc
-
8/10/2019 Options UG
50/234
Page 44
Options in CQG
Vega
The vega is chosen to reflect sensitivity of the spread price with respect to movement of value
of the combined volatility :
.
Theta
Call
,
Put
,
where
Rho
Call
Put
Chi
Chi (as defined in Carmona & Durrleman) denotes the first derivative of option price by
correlation coefficient .
.
TdneFVega rT = )( 11
gcr +=
gpr +=
( ) ( )
( ) ( )
( ) ( 1122212 22ln
2
ln
22 dnT
FednT
XFeT
FdnT
FdnFeT
XFg
TrTrTr
=
+=
++
+=
cT=
pT=
( )
2112 dnTFFe
c Tr =
=
-
8/10/2019 Options UG
51/234
Page 45
Options User Guide
Implied Volatility & Correlation
There is no definite way to calculate both 1, 2given a concrete spot price. It is supposed to
determine the value of the combined volatility by the standard approach of solving theequation numerically as done in Black-Scholes model.
However, it should be possible to calculate implied value of any of three 1, 2, variablesprovided the other two are known. For that purpose the partial derivatives of option value byany of three variables may be required to apply Newtons equation solver, for instance.
Lets denote a selected variable as , which may be either of 1, 2, . The generic form of the
partial derivative of option value is:
.
The expression demonstrates that values calculated with BS model can be used. Substituting
with 1, 2, and the expressions for each of , and can be obtained using the
corresponding partial derivatives of given earlier.
c
( )
=
=
=
11111 Vega
cTdnFe
c BSTr
21
,
ccc
-
8/10/2019 Options UG
52/234
Page 46
Options in CQG
Cumulative Normal Distribution FunctionApproximation
For further reading, we suggest: The Complete Guide to Option Pricing Formulas. ISBN 0071389970.
Handbook of Mathematical Functions. ISBN 0486612724.
Abromowitz and Stegun approximation
The following approximation of the cumulative normal distribution function N(x) producesvalues to within six decimal places of the true value.
When x >= 0
N(x) = 1 n(x)(a1 * k + a2 * k^2 + a3 * k^3 + a4 * k ^ 4 + a5 * k ^5)
when x < 0
N(x) = 1 N(-x)
where
n(x) normal distribution;
k = 1 / (1 + 0.2316419 * x);
a1 = 0.319381530;
a2 = -0.356563782;
a3 = 1.781477937;
a4 = -1.821255978;
a5 = 1.330274429;
Harts approximation
This algorithm uses high degree rational functions to obtain the approximation. This function is
accurate to double precision (15 digits) throughout the real line.
-
8/10/2019 Options UG
53/234
Page 47
Options User Guide
Numerical Methods for Solving Equations
The system offers several methods of the solving of the nonlinear equations.
For further reading, we suggest Numerical Recipes: The Art of Scientific Computing, 3rded.
ISBN-10: 0521880688.
Bisection Method
The bisection method is a simple iterativeroot-finding algorithm.
The methodconvergence is linear,which is quite slow. On the positive side, the method isguaranteed to converge.
Newtons Method
Newton's method, also called the Newton-Raphson method, is an iterativeroot-finding
algorithm.
The methodconvergence is usually quadratic,however it can encounter problems for functionwith local extremes.
Newton's method requests that function isdifferentiable.
Newton Safe Method
Newton Safe method is an iterativeroot-finding algorithm,which combines the bisection and
Newtons methods.
The method, however if function has local extremes convergence can be linear.
Like Newton's method, Newton safe method requests that function isdifferentiable.
Brents Method
Brents method is an iterativeroot-finding algorithm.
This method is characterized by quadratic convergence in case of smooth functions and
guaranteed linear convergence in case of non-smooth or sophisticated functions.
http://en.wikipedia.org/wiki/Root-finding_algorithmhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://en.wikipedia.org/wiki/Derivativehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Root-finding_algorithmhttp://en.wikipedia.org/wiki/Root-finding_algorithmhttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://en.wikipedia.org/wiki/Root-finding_algorithm -
8/10/2019 Options UG
54/234
Page 48
Options in CQG
Numerical Differentiation
The first derivative shall be calculated as
The first derivative represents instantaneous rate of change, which is limit of average rate ofchange where h is the small time interval,
h=the time between point t and point t+1=t (delta t)The secondderivative shall be calculatedas
h
ff
dx
df ii
xx i2
11 +
=
2
11
2
2 2
h
fff
dx
fd iii
xx i
+
+
-
8/10/2019 Options UG
55/234
Page 49
Options User Guide
Trading Options
Trading with CQG IC is explained in detail in ourtrading user guide.
As an options trader, you may want to:
Add a Greek column to DOMTrader (Trading Preferences > Display > Greek column foroptions)
Highlight theoretical value on the DOMTrader (Trading Preferences > Display > PriceColumn)
Select on options model (Trading Preferences > Display > Options)
Use theoretical value to calculate UPL/MVO (Trading Preferences > Display > Status)
DOMTrader and Order Ticket have options-specific components. The current strike price is
displayed, and you can change the model and Greeks directly on the trading application. The
Account Summary area of Orders and Positions also has options-specific data.
Note about options prices on DOMTrader
You may wonder why price calculations sometimes differ between the options window andDOMTrader.
As expected, the price on the options window is calculated using market data and shows the
current value of the Greek for a single price.
DOMTrader offers an entire ladder of prices. Except for the single cell where the last tradeoccurred, other prices are potential prices at which the options contract may be traded later, ifthe market moves in that direction. Because we cannot calculate an actual price for a future
state, we use predictive mathematics to derive those potential prices.
To calculate Delta for a potential price of C.EP U213350 away from the current market (say, at4100), we use the price of the underlying instrument F.EPU2 and other characteristics of the
F.EP market movement that would result in market of C.EP U213350 moving to 4100.
Thus, we are trying to predict what the value of Delta would be then if the option price achieves4100. CQG uses a complex algorithm to make that prediction.
http://www.cqg.com/Docs/Trading_UG.pdf#page=1http://www.cqg.com/Docs/Trading_UG.pdf#page=1http://www.cqg.com/Docs/Trading_UG.pdf#page=1http://www.cqg.com/Docs/Trading_UG.pdf#page=1 -
8/10/2019 Options UG
56/234
Page 50
Options in CQG
Because of this difference in calculation, the prices on the options window may be differentfrom the prices on DOMTrader.
-
8/10/2019 Options UG
57/234
Page 51
Options User Guide
Setting Options Preferences
To set options preferences, click the Setupbutton and then click Options Preferences. Youcan also click the Prefsbutton on the Options toolbar.
To start, select the model and where to apply these preferences. If you select DDE & Operatorvalues, changes apply to other areas where options are used, such as custom studies.
Click the Summarybutton to view, print, and save (.dat file) the current settings.
Click the Defaultsbutton to return to default values.
-
8/10/2019 Options UG
58/234
Page 52
Setting Options Preferences
Other Options preferences include (tabbed area at bottom of window):
View settings allow you to show or hide Greek and implied volatility scales, ordercolumns, and set extended coloring parameters.
Volatility settings allow you to set the implied volatility type, evaluation method foraverage volatility, and select a volatility calculation type.
Interest Rate settings allow you to set the interest rate for various currencies.
Price Filter settings allow you to select which price to use for underlying and option.You can also choose to use most recent settlement prices.
Greeks Scale settings allow you to set the price scale, time direction, and time scaleand to choose percent or fractions for implied volatility and delta and gamma.
Advanced settings allow you to select the underlying contract type and increase days toexpiration.
Model settings allow you to define parameters for each model.
Update Frequencysettings allow you to set the refresh period for average volatility,interest rate, and new/removed contract and to set update delays for theoretical value
and the Greeks.
-
8/10/2019 Options UG
59/234
Page 53
Options User Guide
Setting Options Window View Preferences
View settings allow you to show or hide Greek and implied volatility scales, order columns, and
set extended coloring parameters for old and stale.
Appearance
Select this check box to display the scale setting (percent or fraction) in the header.
Column order
Click the Monthscheck box to arrange the columns by month.
Click the Puts/Callscheck box to arrange the columns so that all calls columns come beforeputs columns.
Extended Coloring: Mark as
Set the threshold for old prices and stale movement.
-
8/10/2019 Options UG
60/234
Page 54
Setting Options Preferences
Setting Options Calculator View Preferences
Degree of Polynomial
Enter a value up to 8. The higher value, the slower the drawing of the graph but the better thecurve fits the Volatility Skew graph.
Points to Plot
Enter a value up to 120. The higher the number, the slower the drawing of the graph but the
higher the definition.
-
8/10/2019 Options UG
61/234
Page 55
Options User Guide
Setting Volatility Workshop View Preferences
Show
Choose the elements to add to the Volatility Workshop display: Yesterday curve, Yest. IVs,
Call/Put curve, or Net Change.
Each of these becomes an additional row in the table about the graph and are displayed on thegraph.
The curves are added to the graph. Yesterdays IV (each options settlement IV) is representedas circles on the graph. Net change is represented as a vertical line between the current IV and
yesterday's settlement IV.
Strikes Range
Expand the curves on the left and right side by a designated percentage. This facilitates
estimating the IVs of options that have not yet been listed. For example, if the range prior to
the expansion was from 1000 to 3000 and the range was expanded on the right side by 10percent, the new range would be from 1000 to 3200 [(.1*(3000 - 1000) + 3000].
-
8/10/2019 Options UG
62/234
Page 56
Setting Options Preferences
X-Axis type
Select the variable represented by the X-axis: Strike Priceor Delta.
Mark as
Set the threshold for old prices, in hours, and stale movement, in percent.
-
8/10/2019 Options UG
63/234
Page 57
Options User Guide
Setting Strategy Analysis View Preferences
Display type
Select whether to display the P&L graph using profit/loss as a function of the underlying price orvalue of the portfolio as a function of price.
-
8/10/2019 Options UG
64/234
Page 58
Setting Options Preferences
Setting Volatility Preferences
Volatility settings allow you to set the implied volatility type, evaluation method for average
volatility, and select a volatility calculation type.
Volatility for calculation
Select one of:
Apply vol surface= 3-D value from the Volatility Workshop
Apply vol curve= 2-D value from the Volatility Workshop
Use IV for Greeks&TheoV = Used in conjunction with the Implied Volatility Type,Traded or Momentary.
Use IV for Greeks= Used in conjunction with the Implied Volatility Type, Traded orMomentary.
Use Average Vol= Used in conjunction with the Average Volatility evaluation method.
The average volatility using Put-Call Separate and Put-Call Combined is calculated bytaking a weighted average of the 2 implied volatilities for the strikes encompassingthe at-the-money-strike.
For example, with the underlying at 1392.00 and the implied volatility of the 1390.00calls at 26.02 and the implied volatility of the 1395.00 calls at 25.42 the average callvolatility would be: .6(26.02) + .4(25.42) = 25.78. This volatility would be used to
value all the calls. The average put volatility would be calculated the same way and
that value would be used to value the puts. If the Put-Call Combined choice wereselected, the call volatility and put volatility would be averaged and that volatility
would be used for all the options series of that particular underlying.
Please note that theoretical value cannot be calculated using implied volatility. If you select the
Use implied volatilitycheckbox, CQG uses implied volatility to calculate all the values excepttheoretical value, where it uses one of the selections from the dropdown list: Put-Call Separate,Put-Call Combined or Historical. However, if the Use implied volatilitybox is not selected, all
the values are calculated using one of the three methods.
-
8/10/2019 Options UG
65/234
Page 59
Options User Guide
Implied Volatility Type
Select one of:
Traded= Matches the options price with the underlying price, based on a time whenthe two prices were in sync, that is, the options price happened no later than 3 hours
after the underlying price. This could lead to a value that is in sync but not current.
Using this value involves taking the synced underlying price (also referred to as thecoherent underlying price), which is the close of the underlying instrument during
the minute prior to the last option tick. However, if the underlying has not tradedduring this minute, the system uses the underlying tick closest to the time of the
option trade, as long as it happened during the current trading day. If the options
price is a closing value, the settlement price for the underlying is used as thecoherent underlying price.
Momentary= Matches the options tick with the nearest tick in the underlying, even ifthe underlying trade happened after the options price. Volatilities calculated this waymay be off by a large amount if the underlying trade took place substantially before orafter the options trade.
If you select this value, the calculation uses the most current underlying price andthe most current options price. Volatilities calculated this way may be off by a largeamount, if the underlying price has changed significantly since the last options tick.
In other words, momentary implied volatility takes the most current underlying tick
without matching it to the time of the options. This may or may not result in thesame volatility as the traded implied volatility.
These selections are global, which means they apply to all models. (Implied volatility selections
made on the Modeltab are only relevant to the selected model.)
Average volatility
Select one of:
Put-Call Separate= Two values, one for the calls and one for the puts, are calculatedand given separately. These values are then used as the volatility input for the selectedoptions model.
Put-Call Combined= The separate call and put volatilities are averaged together andone value is given. This value is then used as the volatility input for the selected optionsmodel.
Historical Volatility= Represents the standard deviation of a series of price changesmeasured at regular intervals. You define the Historical Volatility using either Percent or
Logarithmic price changes. Percent changes assume that prices change at fixed
intervals. Logarithmic changes assume that prices are continuously changing. Historical
Volatility requires a period value. Constant value requires a percentage value. Constant Volatility= If selected, you must also select a percentage for the volatility.
For example, if the selected contract was trading at 1300 and the volatility valueselected was 10%, you would be implying an underlying price of 1300+ or - 10%, i.e.,1170-1430 over the next year.
-
8/10/2019 Options UG
66/234
Page 60
Setting Options Preferences
Setting Interest Rate Preferences
These settings allow you to set the interest rate for various currencies.
First, select the currency using the drop down menu, then select the type of interest rate andset the value.
-
8/10/2019 Options UG
67/234
Page 61
Options User Guide
Setting Price Filter Preferences
These settings allow you to select the options and underlying prices that are used for the
options displays. You can also choose to use most recent settlement prices.
Use Most Recent Settlement Prices
When you click this button, the system disables the other choices and yesterday's settlement
price is used. If the market has already closed for the day, then today's settlement price isused.
Yesterday
Select this button to use yesterdays closing price.
No Filtering
Click this button to use the most current Bid, Ask, Last Trade, or Yesterday's Close as theoperative option price.
Option price and Underlying price
Select the price type for both the Option and the Underlying price: Bid, Ask, Bid/Ask
average, Last Trade, and Yesterdays Close.
If more than one price is selected, the system uses the most current of the selected prices.
For example, if only Last Trade and Yesterday's Close are selected, the last trade appears as
long as that trade took place in the current day's session. Likewise, if Bid or Ask is selected
along with Last Trade, the most recent Bid or Ask appears as long as it is more recent than thelast trade. If not, the last trade appears.
-
8/10/2019 Options UG
68/234
-
8/10/2019 Options UG
69/234
Page 63
Options User Guide
Setting Advanced Preferences
Advanced settings allow you to select the underlying contract type and increase days to
expiration.
Not all options are available for all models:
Black, Black-Scholes, Bourtov, and Garman-Kohlhagen Modifications only
Whaley Modifications and Dividends amount
Merton Modifications, Underlying contract type, Dividends amount
Cox-Ross-Rubinstein All
Contract style
Select Americanor European.
Underlying contract type
Select Futuresor Indices, Stocks, etc. or click the select automaticallycheck box.
Type a value for the percentage of the underlying price for the dividends amount.
Modifications
Type a value for how many days you want to increase the expiration by. You can also use the
arrows. This is useful for contracts that are deliverable or settle after the last trading day.
-
8/10/2019 Options UG
70/234
-
8/10/2019 Options UG
71/234
Page 65
Options User Guide
Setting Update Frequency Preferences
Because Greek values generally change slowly and updating them takes a lot of processing
time, CQG IC offers you the opportunity to set optimal update frequencies based on your
preferences.Update Frequency settings allow you to set the refresh period for average volatility, interest
rate, and new/removed contract and to set update delays for theoretical value and the geeks.
These preference do not apply to the Options Calculator.
Delayed updates for model values
This setting allows you to delay updates for particular model values. Select the check box, then
enter delays, in seconds, for the theoretical value; Delta & Gamma; and Vega, Theta, Rho.
If this check box is cleared, the system updates the Greek and Theoretical values whenever
there is a relevant change in the data.
Refresh period for
Enter refresh periods for Average Volatility, Interest Rate, and New/Removed Contracts.
-
8/10/2019 Options UG
72/234
Page 66
Setting Options Preferences
Updating the Refresh Rate
The refresh rate is different from the update frequency rates set in preferences. While
frequency rates dictate when calculations are updated, the refresh rate dictates when the
particular options window view is updated.
To change the update rate
1. Click the Setupbutton.
2. Click Update Rate.
3. Click the rate you want to set and enter a value for the interval. To stop updates,click the No updatesbutton.
4. Click OK.
-
8/10/2019 Options UG
73/234
Page 67
Options User Guide
Options Window
The Options Window has three views: Standard, Greek, and Theoretical versus Underlying. Youcan customize these views, so that they display information relevant to you.
To open the Options window, click the OptWndbutton on the toolbar. If the button is not
displayed, then click the Morebutton, and then click Options. You can also click the Options
button and then click Options Window.
The Options Window has three views:
Standard
Greek
Theoretical versus Underlying.
The Standard view changes based on the value you want displayed: LPrice, TheoV, Delta,
Gamma, Theta, Vega, IV, Open Int, and Volume.
The title bar indicates which view is active.
-
8/10/2019 Options UG
74/234
Page 68
Options Window
Standard view
Data in the top row includes:
UndPr= underlying price
DTE= number of calendar days until expiration
Exp= expiration date
Vol= default volatility used for calculations, default values is set in Options preferences:
IVS= implied volatility shift, sets the increase or decrease of all implied volatility values
-
8/10/2019 Options UG
75/234
Page 69
Options User Guide
IR= default interest rate calculated by taking 1 near term T-Bill price
Data in the bottom row includes the strike price, the bid or ask price, and then a value based
on your settings. For example, if the LPricebutton is selected, then this value is last price netchange. If the Thetabutton is selected, last price and theta is displayed.
In this example:
pink text = yesterday extended colors
red text = daily net down
green text = daily net up
Colors can bechanged.
-
8/10/2019 Options UG
76/234
-
8/10/2019 Options UG
77/234
Page 71
Options User Guide
Theoretical versus underlying (T/U) view
The T/U view displays data according to strike price.
Data in the top row includes:
UndPr= underlying price
DTE= number of calendar days until expiration
Exp= expiration date
Vol= default volatility used for calculations
IVS= implied volatility shift, sets the increase or decrease of all implied volatility values
IR= default interest rate calculated by taking 1 near term T-Bill price
-
8/10/2019 Options UG
78/234
-
8/10/2019 Options UG
79/234
-
8/10/2019 Options UG
80/234
Page 74
Options Window
Pause button
Pauses data updates and value recalculations.
Options displays constantly update during trading hours. Consequently, when the markets are
active, the displays could be changing quite rapidly, not allowing you to fully digest the effectsof each change. To alleviate this problem, you can pause without losing data.
Right-click this button to update the data immediately and update the rate.
Settle button
Click this button to view options data based on the most recent settlement price rather than themost recent tick data.
Prefs button
Click this button to open theOptions Preferenceswindow.
Cost button
Click this button to display the notional value of the option premium. Click it again to return to
the regular display. Works in conjunction with the multiplier button.
Multiplier button
Type a number to multiply the notional value of the option premium by. Displayed only whenthe Costbutton is on.
-
8/10/2019 Options UG
81/234
Page 75
Options User Guide
Customizing Columns
You are able to customize the columns displayed in the Greek view.
1. Click the Setupbutton.
2. Click Customize Columns.
3. Select and clear the check boxes for the columns you want to show and hide.
4. To move the columns, use the Move to Top, Move Up, and Move Downbuttons.
-
8/10/2019 Options UG
82/234
Page 76
Options Window
Column Names
Column Label Full Name
Ask Ask Price
Ask Vol Ask Volume
Bid Bid Price
Bid Vol Bid Volume
Delta Delta
DeltaNC Delta Net Change
Gamma Gamma
GammaNC Gamma Net Change
Imp Vol Implied Volatility
ImpV NC Implied Volatility Net Change
Net Chg Net Change
OI Open Interest
Price Price
Pr-Theo Price - Theoretical Value
Rho Rho
Rho NC Rho Net Change
Theo NC Theoretical Value Net Change
TheoVal Theoretical Value
Theta Theta
ThetaNC Theta Net Change
TickVol Tick Volume
Time Time
Und Pr Underlying Price
Vega Vega
Vega NC Vega Net Change
-
8/10/2019 Options UG
83/234
Page 77
Options User Guide
Column Label Full Name
Volume Volume
Vol Crv Volatility Curve Value
-
8/10/2019 Options UG
84/234
Page 78
Options Window
Changing the Order of Columns
To toggle the order of the columns between months and puts/calls for the LPrice, TheoV, Delta,
Gamma, Theta, Vega and IV views:
1. Click the Setupbutton.
2. Select Change Order. A months view changes to puts/calls and a puts/calls viewchanges to months.
Months view:
Puts/Calls view:
-
8/10/2019 Options UG
85/234
-
8/10/2019 Options UG
86/234
Page 80
Options Window
Changing the Display Type
In addition to changing the display of the standard view options window with the toolbar
buttons, you can right-click the Setupbutton and then click the display you want:
-
8/10/2019 Options UG
87/234
Page 81
Options User Guide
Opening Another Application from an OptionsWindow
Right-click the options window, and then click an application name, including: Time & Sales
Snap Quote
Chart
Options Calculator
Options Graph
Volatility Workshop
-
8/10/2019 Options UG
88/234
Page 82
Options Window
Setting What If Options Parameters
On the Options Parameterswindow, you can change any or all of several variables for
different series: Underlying Price, Volatility, Implied Volatility Shift, Interest Rate, Days to
Expiration (days until the most distant expiration selected in the Apply to area), and Date.
1. Click the WhatIfbutton. You can also right-click on the Options window.
2. Select the series to which the changes are applied from the Apply tocolumn. Clickthe All buttonto select every series in the selected commodity.
3. Enter the changes in the What ifcolumn.
Click the Newtab to create another What If set.
Click the Actualsbutton to clear any What Ifs that have been applied to the options window.
-
8/10/2019 Options UG
89/234
-
8/10/2019 Options UG
90/234
Page 84
Options Window
Placing Orders from the Options Window
1. Right-click on the options window.
2. Click Place an Order.
The Order Ticket, Simple Order Ticket, or DOMTrader opens depending on your
system settings. (Setup > System Preferences > Misc > Preferred Order Entry
Display).
-
8/10/2019 Options UG
91/234
Page 85
Options User Guide
Options Calculator
CQGdesigned the Options Calculator to calculate and display the theoretical and Greek valuesof an option contract based on user-defined What if values. You can display outputs for a singleset of What if values or in graphical form over a continuously varying range of What ifs.
To open the Options Calculator, click the OptCalcbutton on the toolbar to launch the Options
Calculator. If the button is not displayed, click the Morebutton, and then click Options
Calculator. You can also click the Optionsbutton and then click Options Calculator.
-
8/10/2019 Options UG
92/234
Page 86
Options Calculator
Options Calculator Components
The Options Calculator includes these areas:
Title bar
Contract area
Inputs area
Calculate area
-
8/10/2019 Options UG
93/234
Page 87
Options User Guide
Graph area
-
8/10/2019 Options UG
94/234
Page 88
Options Calculator
Options Calculator Toolbar
These buttons are common to both the options window and the options calculator:
Actuals
Puts
Calls
Prev/Next
Pause
Settlement
Prefs
The Options Calculator toolbar also includes these buttons:
FullScr button
Displays the Options Calculator graph across the entire width of the CQG window, hiding the
Contract and Input sections.
Rescale button
Re-adjusts the scales.
Futures button
Switches from an FX OTC view to a futures view.
FXOTC button
Click this button to view OTC Foreign Exchange contracts.
The CQG FX OTC Options Calculator allows users to evaluate several types of OTC cross
currency options. Currently users can evaluate 4 types of options: Vanilla OTC Spot, ExoticVanilla Barrier, Exotic Binary AON and Exotic Lookback.
To use the FX OTC Options Calculator, you must specify:
a model
underlying asset price
strike price
interest rate
volatility
days until expiration
specific model parameters.
-
8/10/2019 Options UG
95/234
Page 89
Options User Guide
When these values are given, the Options Calculator evaluates the theoretical value or impliedvolatility (if options price was specified) and all Greeks for the "virtual contract."
-
8/10/2019 Options UG
96/234
Page 90
Options Calculator
Using the Options Calculator
Using the [Tab]key (to move to the next cell) and[Shift] + [Tab]keys (to move to the
previous cell) keys facilitates moving around in the Options Calculator.
Using the Options Calculator involves:
1. Selecting the desired instrument symbol.
2. Inputting the desired series.
3. Selecting a model.
4. Inputting the What if values (if desired).
5. Choosing a type of graph (top tabs).
6. Selecting a view (bottom tabs).
Selecting a Symbol
To begin using the Options Calculator you must:
Enter the commodity symbol without any month indicator.
Example: JY
Selecting the Class and Expiration Month
Once you have entered the desired symbol, a drop-down list appears in the Option row of the
Contract section.
Select the desired class and expiration month from the drop-down list associated with the
Option row in the Contract section.
Selecting the Strike
After you have selected a symbol, class and expiration month, a drop-down list appears in the
Strikerow.
Select the desired strike price.
After a series is selected, the Actualscolumn is filled in with the most recent values.
Note: Prices indicated by an asterisk in the Actuals column are yesterday's values.
-
8/10/2019 Options UG
97/234
Page 91
Options User Guide
Selecting a Model
Options pricing models produce theoretical values for an option contract based on five inputs:
Underlying Price, Strike Price, Time