Chp07

Copyright K.Cuthbertson, D.Nitzsche.

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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

Call Options

Put Options

Financial Engineering

Topics


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Uses of Options


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

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

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 can simply 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 option premium and ‘downside’ losses are limited

Insurance - can limit ‘downside’ outcome but allows most of the ‘upside potential’

Delta Hedging - ensures that the value of your portfolio is unchanged (over say 1-week) - I.e. no ‘upside’ or ‘downside’

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 at any 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


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Call Options


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Buy ( “long”) European Call Option

Then you have the choice of buying the underlying asset (stock) at a future 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


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

Profit

K=80

83 88 ST

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 .


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

If ST > K 88 > 80

Exercise the option (“in-the-money”)

Gross profit = ST - K = 88 - 80 = $8

Net profit = ST - K - C = $8 - $3 = $5

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

If ST < 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


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SPECULATION

Because you only pay about $3 to ‘gamble’ on the future stock price, which will have a current value of around $80, then options provide ‘leverage’ for a speculator.

The ‘downside’ is also limited to the call premium paid.

Summary: Payoff from Call at Expiry


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HEDGER: Obtains INSURANCE.

If the stock price at maturity (T) is high (e.g. ST = 88) then the pension fund ‘exercises the option’ at the CBOT and pays only K=80 for the stock.

BUT if the stock price is low (e.g. ST = 60) then the pension fund ‘walks away’ from the option contract (ie. does not exercise at K=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=80 but it can take advantage of lower stock prices should these arise.

For this ‘flexibility’ the pension fund pays the call premium of $3 (today).

Summary: Payoff from Call at Expiry


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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 to excercise the option at expiry

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

Write(Sell) European Call Option


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K=80 83 88 ST

Strike Price, K = 80

$3 Call Premium

-$5

0-1

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

Figure 2 Sell( Write) a European Call Option


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Put Options


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Buy ( Long) European Put Option

Have the choice of selling the underlying asset (stock) at a future 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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Buy a PUT OPTION = Trial Separation

BUCKSIDE


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Exercise the Put = DIVORCE

BUCKSIDE( Fin )


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ST

Profit

K=70680

2

Strike Price K= $ 70

65Put Premium

+3 0

-1

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

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

Figure 3 Buy (Long) : European Put


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ST

Profit

K=70680

-3

Strike price K= $ 70

Stock price at expiry, ST = 65

65Put Premium

+2

+1 0

Figure 4 Sell( Write): European Put


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INSURANCE

BUYING, Calls and Puts allow you to ‘lock in’ a (strike) ‘price’ in the future, by paying the option premium today.

This ‘price’ can be for a company stock, stock-index,T-bond, currency or an interest rate (e.g. to ‘insure’ the maximum cost of borrowing on a existing loan).

You may also choose to NOT EXERCISE the option, if it is better to do the deal in the ‘spot market’.

SPECULATION (‘LEVERAGE’)

Bull market - buy a call

Bear market - buy a put

SUMMARY: BASICS OPTIONS


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Financial Engineering


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+1

Long Put

plus

Long Stock

equals

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


Financial Engineering: Leeson’s Short Straddle Short (=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 is either 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” and large losses).

K


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END OF SLIDES


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