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.