Suppose you are an option trader and are now considering the options on the shar
ID: 2790729 • Letter: S
Question
Suppose you are an option trader and are now considering the options on the shares of HSBC.
The current stock price of HSBC is $60. It is expected that the stock price of HSBC will go up by 12% or down by 12% over each of the next two three-month periods. The risk-free interest rate is 3% per annum with continuous compounding.
Required
a Determine the value of a six-month European call option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. (12 marks)
b Determine the value of a six-month European put option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. (6 marks)
c Determine the value of a six-month American put option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. Explain whether the American put option should be exercised at the end of the first three-month period. (12 marks)
Explanation / Answer
A.)Determine the value of a six-month European call option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. (12 marks)
Basics of Option Pricing:-
An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (called a strike price or an exercise price) at or before the expiration date of the option. Since it is a right and not an obligation, the holder can choose not to exercise the right and allow the option to expire. There are two types of options: call options and put options.
Call and Put Options:
A call option gives the buyer of the option the right to buy the underlying asset at a fixed price, called the strike or the exercise price, at any time prior to the expiration date of the option. The buyer pays a price for this right. If at expiration, the value of the asset is less than the strike price, the option is not exercised and expires worthless. If, on the other hand, the value of the asset is greater than the strike price, the option is exercised - the buyer of the option buys the asset [stock] at the exercise price. And the difference between the asset value and the exercise price comprises the gross profit on the option investment. The net profit on the investment is the difference between the gross profit and the price paid for the call initially.
For a call, the net payoff is negative (and equal to the price paid for the call) if the value of the 2 underlying asset is less than the strike price. If the price of the underlying asset exceeds the strike price, the gross payoff is the difference between the value of the underlying asset and the strike price and the net payoff is the difference between the gross payoff and the price of the call
As per above example: it come to be 0.26.
B. Determine the value of a six-month European put option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. (6 marks)
European put option:-
A put option gives the buyer of the option the right to sell the underlying asset at a fixed price, again called the strike or exercise price, at any time prior to the expiration date of the option. The buyer pays a price for this right. If the price of the underlying asset is greater than the strike price, the option will not be exercised and will expire worthless. If on the other hand, the price of the underlying asset is less than the strike price, the owner of the put option will exercise the option and sell the stock a the strike price, claiming the difference between the strike price and the market value of the asset as the gross profit.
Again, netting out the initial cost paid for the put yields the net profit from the transaction. A put has a negative net payoff if the value of the underlying asset exceeds the strike price, and has a gross payoff equal to the difference between the strike price and the value of the underlying asset if the asset value is less than the strike price.
As per above example: it come to be 9.91.
C.Determine the value of a six-month American put option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. Explain whether the American put option should be exercised at the end of the first three-month period. (12 marks)
American Versus European Options: Variables Relating To Early Exercise A primary distinction between American and European options is that American options can be exercised at any time prior to its expiration, while European options can be exercised only at expiration. The possibility of early exercise makes American options more valuable than otherwise similar European options; it also makes them more difficult to value. There is one compensating factor that enables the former to be valued using models designed for the latter. In most cases, the time premium associated with the remaining life of an option and transactions costs makes early exercise sub-optimal. In other words, the holders of in-the-money options will generally get much more by selling the option to someone else than by exercising the options. While early exercise is not optimal generally, there are at least two exceptions to this rule. One is a case where the underlying asset pays large dividends, thus reducing the value of the asset, and any call options on that asset. In this case, call options may be exercised just before an ex-dividend date if the time premium on the options is less than the expected decline in asset value as a consequence of the dividend payment. The other exception arises when an investor holds both the underlying asset and deep in-the-money puts on that asset at a time when interest rates are high. In this case, the time premium on the put may be less than the potential gain from exercising the put early and earning interest on the exercise price.
As per above Call option example: it come to be 0.26. If stcok rise, early exercise. If down , expriation exercise.
As per above Put option example: it come to be 14.14. If stcok rise, expriation exercise.If down, early exercise.