1. For the situation considered in Example 13.1, page 18, what is the value of a 1-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call parity.

2. A stock price is currently $50. Over each of the next two 3-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a 6-month European call option with a strike price of $51?

3. The volatility of a non-dividend-paying stock whose price is $78, is 30%. The risk-free rate is 3% per annum (continuously compounded) for all maturities. Calculate the following when a 2-month time step is used:

a. What is the percentage up movement?

b. What is the percentage down movement?

c. What is the probability of an up movement in a risk-neutral world?

d. What is the probability of a down movement in a risk-neutral world?

e. What is the value a 4-month European call option with a strike price of $80 given by a two-step binomial tree? Draw your binomial tree