Introduction to Financial Engineering

Aashish Dhakal

Week 5: Options: Plain Vanilla, Exotics & Strategies

Our Plan

1. OPTION

2. PLAIN VANILLA

3. EXOTICS

4. STRATEGIES

A tale of Risk………..Case1:

You are Head Corporate Treasury

You have just imported a machine, worth $10 lakh on 180 days credit @ 0% interest.

Dollar current rate is Rs98/$.

IS THE DEAL RISK FREE….??

Case2:

Your company has surplus cash for investment.

You are no Warren Buffet, … but you would like to earn a return of 15% on investment.

You think you have spotted bargain in Infosys, currently quoting @ Rs 1000.

You believe the price will rise to Rs 1075 in six month. IS THIS DEAL RISK FREE?

A tale of Risk………..Transparently, both deal hold some quantum of risk….. YES….

So what do you do to safeguard your company?

You have three choices, in each case.

CHOICE 1: FORWARD

CHOICE 2: FURTURE

CHOICE 3: OPTION

OK,,,, So Now,, What Do these three choice give us so that we can safeguard our company??

Derivative Instrument

Contractual Instruments: Derivatives

There is no universally satisfactory answer to the question of what a derivative is,

however lets have one explanation ......

A derivative is a ‘financial instrument or security

whose payoff/value depends on

another financial instrument or security’ ...i.e... the payoff or the value is derived from

that underlying security

They are agreements or contracts between two parties

Contractual Instruments: Derivatives….

Contract between two Parties….

Of some financially tradable things

at some point of time

At the rate defined in the contract..

And this contract is now contractual instrument….. Named as derivative….

And the value of this contract,, now named as derivative is determined by the value of things

of which dealing is being made.

Value of Derivative: ExampleYOU + Few Friends: Want to watch a concert Scheduled next month

Each Ticket Cost Rs 1000

You call and find out tickets are fully sold

An Acquaintance, who is a part of concert team, gives you a reference letter

Under which, if you show this letter : you can BUY THREE TICKTETS Paying RS 1000 Per

SO WHAT DO THIS LETTER GIVES TO US?

Right to Buy Tickets

Do the letter itself have a value ?

NO, it itself have no market value

Value of Derivative: Example Let Us Now Move Towards concert Day:

Concert Day draws closer

Tickets are being sold at grey market @ 1500

NOW: at this point your letter attains value. ISTNT IT??

Thanks to the letter, now you can buy a tickets, now available in market @ 1500

THE LETTER IS NOW WORTH Rs (1500-1000) X 3 = Rs1500

Suppose a week before concert the price of the grey market shoots to 2000 than the worth of the

letter will be: 3000…. ISNT IT??

Value of Derivative: Conclusion Lets draw five simple tenets from this example:

The VALUE of the letter changes with the Price of the TICKET.

The letter derives its value from the value of ticket. Hence it is called “Derivative” instrument.

The letter gives you a right to buy the tickets.

The underlying asset is TICKET

The letter does not constitute ownership. It is instead a promise to convey ownership.

Options: Definition:

An Option is an CONTRACT between TWO PARTIES

under which the BUYER of the OPTION, BUY the RIGHT

(but don’t hold Obligation )

to buy or sell a standard quantity (contract size) of

a financial instrument (underlying Asset)

At or before the pre determined date (expiry date)

At a Price Determined in advance (exercise price or Strike price)

Buyer/Holder

Seller/Writer

Contract

BUY : RIGHT

HOLD : OBLIGATION

To Buy

/ Sell

To Buy

/ Sell

Asset

Option TypeOption

CALL Option:

Here the Option Buyer BUYRIGHT TO buy the Asset

PUT Option:

Here the Option Buyer BUYRIGHT TO Sell the Asset

Option Example . WIPRO Share:

@ 700 Per share

??Will

Rise to 900

??Will

Fall to 500

BUYS OPTION From MR A

RIGHT TO BUY in FUTURE (say) @ 725 (Between 700 – 900)

So if Price go to 900 he gains = 900 – 725

Here The OPT is CALL OPT

BUYS OPTION From MR A

RIGHT TO Sell in FUTURE (say) @ 625 (Between 700 – 500)

So if Price fall to 500 he gains = 625 – 500

Here The OPT is PUT OPTWANNA Take Adv

Thrg OPTION

ONE SIMPLE FORMULA:

BUY LOW

SELL HIGH.

SO DO YOU GET THE OPTION IN FREE??

NOOOO……

For to get an OPTION (i.r RIGHT) to BUY or SELL Asset

YOU Have to PAY some additional Charge……..

This is what we call PREMIUM

Premium are paid at an initial phase of buying option.

In the money / At the money / Out of the Money

If exercising the OPTION gives you:

A. PROFIT “In the Money”

B. LOSS “Out of the Money”

C. NULL “At the Money”

Exercise Price (EP) Market Price (MP) Situation CALL BUYER(Rt to Buy)

PUT BUYER(Rt to Sell)

40 45 EP < MP In the money (ITM) Out of the Money

40 40 EP = MP At the money (ATM)

At the money

40 35 EP > MP Out of the Money (OTM)

In the money

BUY LOW SELL HIGH

AT EXPIRY: Option Delivery Process

What Happen On Expiry?

A. Exercise If the Option, at the expiry is “ITM”

B. Expire / Lapse If the Option, at the expiry is “OTM” & “ATM”

Relationship CALL buyer PUT BuyerEP > MP (40 > 35) Lapse Exercise

EP = MP (40 = 40) Lapse Lapse

EP < MP (40 < 55) Exercise Lapse

Rule 1Rule 2

Party Gains if

Call Buyer Price RISES BULLISHPut Buyer Price FALLs BEARISHCall Writer Price FALLs BEARISHPut Writer Price RISES BULLISH

VALUE OF OPTION: Call A call option on H ltd Stock has an exercise price of Rs 20. If, the stock price on expiry ranges

from between 18 to 24 with interval of 2. Compute the value of call.

Particulars I II III IV

Market Price 18 20 22 24

Exercise Price 20 20 20 20

STATUS OTM ATM ITM ITM

Action Lapse Lapse Exercise Exercise

VALUE / Gross Pay Off

0 0 2 4

Right to BuyYOU ALWAYS BUY AT LOW

I f market gives you Low you buy at market & if Opt gives you at Low You buy at OPt

PAY OFF & PAY OFF GRAPH Gross Pay Off = Value of Option

Net Pay Off = Value of Option Less Premium

Suppose in last example, if the Premium to buy the option is Rs 1 than Calculate the net Pay off

Particulars I II III IVVALUE / Gross Pay Off 0 0 2 4

Premium (1) (1) (1) (1)

Net Pay off (1) (1) 1 2

Pricing of Option : Black – Scholes Model

Initial to Black Scholes Model, two model of valuation of Option came in existence:

A. Risk Neutral Model: assumed that option with one year life, price changes in stock happens only once a year

B. Binomial Model: It is an advancement of Risk Neutral Model. It kept the life of option as similar ONE YEAR but Assumed That Price Change TWICE ( every 6 mth).

BUT, We know that the price of the stock are volatile and keeps changing continuously.

So considering the said fact, there came an existence of new Model, DRAFTED Out by FISHER BLACK & MYRON SCHOLES named as Black Scholes Model.

Value = Current MP x N(d1) – PV of Exercise Price x N(d2) = So x N(d1) – (E x e-rt ) x N(d2)

Pricing of Option : Black – Scholes Model

Where,

d1 = [ Ln {So/E} + { r + 0.5 σ2} t ] / {σ √t}

d2 = [ Ln {So/E} + { r - 0.5 σ2} t ] / {σ √t}

AND,

Ln = natural Log

σ = Standard Deviation of continuous compounding rate

t = Time remaning before expiration

r = continuous compounding risk free rate of return

N = Cummulative area of normal distribution evaluated at d1 & d2

Option Strategies: A. Straddle

B. Synthetic Future

C. Caps - Floors

StraddleStraddle involves simultaneous Purchase or Sale of Option with same strike price and same expiry date.

i.e. Under this strategy:

A. You Purchase (Buy/Hold)

OR

B. You Sell ( Write)

So we have two Broad Type of Straddle:

Call

Put

You BUY = Long Straddle

You Write = Short Straddle

Call PutBuy

Sell Call Put

Straddle :Concept Example A call option on a stock with an exercise price of Rs. 70 is available for Rs. 6 while a put option on the same stock with same expiration date and same exercise price is selling for Rs 8. using these options create a Long Straddle. Draw the Pay Off Table & Graph.

Ans: (S=Market price)

LONG STRADDLE BUY = CALL + PUT

Relation Put Holder Call Holder GPO Premium NPO BEP

S < E1(S < 70)

ExerciseE1 - S

LapseNil

E1 - S (14) (70 – S) -14 70-14 = 56

S = EP(S = 70)

LapseNil

LapseNil

Nil (14) (14) NA

E1 < S(70 > S)

LapseNil

ExerciseS – E1

S – E1 (14) (S –70 ) -14 70+14=84

Straddle :Concept ExampleS.N Stock Price What Happens

a 1 to 55 Decreasing Profit

b 56 BEP

c 57 to 70 Increasing Loss

d 71 to 83 Decreasing Loss

e 84 BEP

f 85 to … Increasing Profit

Synthetic StraddleStraddles can be created synthetically Where,

instead of buying calls and puts together,

we create the same risk profile by combining

(calls or puts) with a (long or short position in the stock).

Synthetic Future A synthetic futures contract comprises call options accompanied by put options in order to imitate the attributes of a futures contract.

In order to be effective, the strike price and expiration date must be identical.

A synthetic long futures contract can be simulated using a short put option in conjunction with a long call option.

EG: a synthetic long futures contract on stock XYZ would comprise a put option and a call option as described, both of which would have the same expiration date of (e.g. 31 December 2015) and strike price (e.g. $75).

Synthetic Long FC CALL LONG(Buy) PUT Short(Sell)

Synthetic Long Future

Strike Price

i.e. Long Call

Synthetic Future A synthetic short futures contract can be replicated by placing a long put option accompanied by a short call.

Synthetic Short FC CALL Short(Sell) PUT LONG(Buy)

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