4. A stock index is currently trading at 50. Paul Tripp, CFA, wants to value 2-year index options using the binomial model. The stock will either increase in value by 20% or fall in value by 20%.

The annual risk-free interest rate is 6%. No dividends are paid on any of the underlying securities in the index.

a. Construct a two-period binomial tree for the value of the stock index.

b. Calculate the value of a European call option on the index with an exercise price of 60.

c. Calculate the value of a European put option on the index with an exercise price of 60.

d. Confirm that your solutions for the values of the call and the put satisfy put-call parity.