You start working for the Derivatives Desk of a commercial bank. On your first day, you are given the job of determining the value of call and put options written on a stock index. The following is the information you have gathered to value the option contracts:
i. Currently, the stock index value is equal to 50.
ii. The options you are asked to value have a two-year expiration.
iii. You are asked to use the two-period binomial model to value the options.
iv. Market analysts have a consensus forecast that the stock index will either rise in value by 20% or drop in value by 20%.
v. The annual risk-free rate is 6%.
vi. The stock index is made up of non-dividend paying stocks.
a. Construct a two-period binomial tree for the value of the stock index.
b. Calculate the value of a European call option written on the index. The call option has an exercise price of 60.
c. Calculate the value of a European put option written on the index. The put option has an exercise price of 60.
d. Based on your solutions from parts (b) and (c), confirm that the values of the call and put satisfy the putcall parity