Quantitative Finance

Lecture 8

Options & Strategies

Options

A contract giving the owner the right but no obligation to buy or sell the underlying asset for a fixed price

Call Option

Gives the owner the right to buy an asset for a fixed price

Put Option

Gives the owner to sell an asset for a fixed price

European Option

The option can only be exercised ‘at’ expiry

American Option

The Option can be exercised at any time before and including expiry

Payoff

Vanilla Options

American and European type options are called Vanilla Options

Exotic Options

These may differ in terms of payoffs OR exercise time

The Payoff for a European Call Option is

The Payoff for a European Call Option is

Gain

Gain is the payoff modified by premium paid for the option

For the buyer

European Call

European Put

For the seller

European Call

European Put

Time Value of Options

At time t the intrinsic value of a call option with strike price X is equal to and the intrinsic value of a put option is

The time value of an option is the difference between the time value of an option and its intrinsic value

EXAMPLEStrike Price Intrinsic Value Time Value Option Price

Call Put Call Put Call Put

110 15.2

3

0 3.17 2.84 18.4 2.84

120 5.23 0 6.46 12.2

7

12.2

7

6.46

130 0 5.23 6.78 6.78 6.78 9.64

Why trade in options

Why would one trade in options?

Depending on one’s market view, whether it would rise or fall or, whether it would change or not change, options can be used to hedge risk

We will examine strategies that make use of these different scenarios

Speculating and Gearing

Consider buying a far out of money option, this would usually not cost much

If it expires worthless you lose the small amount you paid for it

If there is a substantial move in the underlying you gain a large profit relative to the initial amount

This is called gearing or leveraging

Example

Suppose a stock is priced at $666 on 14th April , The cost of a 680 call option with expiry 22nd August is $39. If one’s market view is that the stock price will rise sharply (say to $730 by mid August) consider the following Buy 1 stock at $666, it would yield a return

Buy an option for $39, at expiry exercise the option to receive the stock for 680, the return then is

Bull and Bear Spreads

This option strategy has a payoff similar to binaries.

A strategy involving options of the same type (calls or puts) is called a spread.

With calls its called a bull call spread

With puts its called bull put spread

The payoff for a bull call spread with strikes E1 and E2 is

A bull spread will be used by an investor who has a moderately bullish view on the market

Example

Suppose one buys a call with strike of 100 and writes one with strike of 120 and the same expiry

The payoff is 0 below 100, 20 above 120 and linear in between

Straddles and Strangles

A straddle consists of a put and a call with the same strike.

Such a strategy is used by some who anticipates the price of the underlying to change

Someone with the opposing view will ‘sell’ the straddle

A strangle is similar to the straddle except the strikes of the call and put are different

Risk Reversal

This strategy involves a long call with a strike above the current spot, and a short put with a strike below the current spot with the same expiry.

Protects against unfavorable downward price movements but limits the profits from upward price movements

Butterflies and Condors

A strategy involving purchase and sale of options with three different strikes is called a butterfly spread.

A strategy involving options with four different strikes is called a condor spread.