chp07 options markets

8/13/2019 Chp07 Options Markets

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Copyright K.Cuthbertson, D.Nitzsche. 1

Version 1/9/2001

FINANCIAL ENGINEERING:DERIVATIVES AND RISK MANAGEMENT(J. Wiley, 2001)

K. Cuthbertson and D. Nitzsche

LECTURE

Options Markets


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Uses of Options


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An Option gives you the right (but not the obligation) tobuy (or sell) something at some time in the future, at a(strike) price agreed today.

For this privilege you pay the option (price) premiumtoday.One way they differ from futures is

If the deal is favourable to you then you will take

delivery BUT if you do not want to go through with the deal(because it is not advantageous to you), then you cansimply do nothing and walk away .

Uses of Options


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Something in the options contract can be

Shares of AT&T

Stock index (S&P500)

T-bond

Currencies

Gold/Silver (index)

Interest rates

Uses of Options


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Speculation - provide leverage- only pay small optionpremium and downside losses are limited

Insurance - can limit downside outcome but allows most ofthe upside potential

Delta Hedging - ensures that the value of your portfolio isunchanged (over say 1-week) - I.e. no upside ordownside

Arbitrage - ensures there are no (v. few) miss-priced options(too advanced for this course)

Uses of Options


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When options are combined with other options or other assets

(e.g. stocks) then this is known as financial engineering

European Option only be exercised at maturity

American Option can be exercised at any time (eg. before maturity).

BUT you can sell/buy any existing option to another person atany time (I.e. prior to expiration/maturity)

If you buy and later sell the option then delivery (of the share)TO YOU is cancelled (by the Clearing House, CBOT)

Uses of Options



Call Options



Buy ( long) European Call Option

Then you have the choice of buying the underlying asset (stock) at afuture date, at a (strike) price which is fixed today

For this privilege you pay the ( call ) option premium \ price (today)

OR Acquire the right, but not an obligation,

to purchase the (underlying) asset at a

specified future date(expiration \ expiry \ maturity date)

for a certain price ( strike \ exercise price)

and in an amount ( contract size)

which is fixed in advance.

Buy European Call Option



Figure 1 Buy One European Call Option (Underlying asset = stock)

Profit

K=80

83 88 S T

Strike Price, K = 80

$5

Call

Premium $3

0

+1

Speculator: Buys call if thinks S will rise in the future (above K=80)

Hedger: Pension fund wants to buy stock in the future and fears a

rise in S. Locks in a MAX price of K .



Each call option contract is for delivery of 100 shares (but callpremium is based on one share )

If S T > K 88 > 80

Exercise the option (in-the- money)

Gross profit = S T - K = 88 - 80 = $8Net profit = S T - K - C = $8 - $3 = $5

That is net profit = $500 per contract (and upside is unlimited)

If S T < K Do not exercise the option (out-of-the-money)

Loss = C (100) = $300

Speculators loss is limited to $300 per contract (ie.e insurance )

Profit from Call at Expiry



SPECULATIONBecause you only pay about $3 to gamble on thefuture stock price, which will have a current value ofaround $80, then options provide leverage for a

speculator.

The downside is also limited to the call premiumpaid.

Summary: Payoff from Call at Expiry



HEDGER: Obtains INSURANCE.

If the stock price at maturity (T) is high (e.g. S T = 88) then thepension fund exercises the option at the CBOT and pays onlyK=80 for the stock.

BUT if the stock price is low (e.g. S T = 60) then the pension fundwalks away from the option contract (ie. does not exercise atK=80) and simply buys the stock in the spot market (e.g. NYSE)at 60.

Pension fund has insured that the max. price it will pay is K=80but it can take advantage of lower stock prices should thesearise.

For this flexibility the pension fund pays the call premium of $3

(today).

Summary: Payoff from Call at Expiry



Sell ( = write ) European Call Option Acquire an obligation to sell

the (underlying) asset to the buyer

if the buyer decides to exercise the option (and you are still

holding a written call).

The writer of the option must deliver if the long decides toexcercise the option at expiry

Paradoxically the writer of an option, does not have anoption/choice AT MATURITY, ( but before maturity the writerhas the option to close out her position, with another trader)

Write(Sell) European Call Option



K=80 83 88 S T

Strike Price, K = 80

$3Call

Premium

-$5

0-1

Writer: Has to pay an initial margin (e.g. 50% of current value ofstocks, underlying the contract + the option premium)

Figure 2 Sell( Write) a European Call Option



Put Options



Buy ( Long) European Put Option

Have the choice of selling the underlying asset (stock) at afuture date, at a (strike) price which is fixed today

For this privilege you pay

the ( put ) option premium \ price

OR

Acquire the right, but not an obligation,

TO SELL the (underlying) asset at a

specified future date(expiration \ expiry \ maturity date)

for a certain price ( strike \ exercise price)

and in an amount ( contract size)

which is fixed in advance.

European Put Option


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Exercise the Put = DIVORCE

BUCKSIDE( Fin )



ST

Profit

K=70680

2

Strike Price K= $ 70

65Put Premium

+30

-1

Speculator: Buys put if thinks S will FALL in the future

Hedger: Pension fund ALREADY HOLDS STOCKS and in the future, fearsa FALL in S. Locks in a MIN PRICE of K, at which to sell the shares. Butif S does not fall blow K=70 , then walks away and sells shares in the spotmarket (e.g. NYSE)

Figure 3 Buy (Long) : European Put



ST

Profit

K=70680

-3

Strike price K= $ 70

Stock price at expiry, S T = 65

65Put Premium

+2

+10

Figure 4 Sell( Write): European Put


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FinancialEngineering


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Long Put

plus

Long Stockequals

Long Call

0

+1 +1

0

-1

Basis of Put-Call Parity: P + S = C + Cash [= K/(1+r)]

Use: Pension Fund hedging its stock holding when it fears a fall in stock prices(over the next 6 months) and wishes to temporarily establish a floor value (=K)but also benefit from any stock price rises.

(see Long Put above)

Financial Engineering: Synthetic Call Option


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Copyright K.Cuthbertson, D.Nitzsche.

Financial Engineering: Leesons Short StraddleShort (=sell) Call

plus

Short(=sell) Put

equals

Short Straddle

0-1

+10

-1+1

Profit

0

You are initially credited with the call and put premia C + P (at t=0) but if at expiry if there ieither a large fall or a large rise in S (relative to the strike price K ) then you will make a loss

(eg. Leeson s short straddle : Kobe Earthquake which led to a fall in S = Nikkei -225 andlarge losses).

K


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