1. You are given the following information: (use continuous compounding).
Current stock price
$100
Strike price
$100
Annual Volatility (σ)
25%
Annual Risk-Free rate
5%
Time to maturity
3 months (0.25 years)
Time step (Δt)
1 month (1/12 years)
Up parameter (U)
Down parameter (D)
1/U
Compute the current value of a European call option.
2. A look back option is a call option that allows the holder to buy the stock at the minimum stock price that occurred over the period to expiration. Suppose, S0 = $129, U = 1.5, D = 0.5, and R = 1.1, use a 3-period binomial model and find the price of such a contract?
3. You are provided with the following information:
S0 = $129, X = $80, U = 1.5, D = 0.5, and R = 1.1
a) Compute the value of a call option using the two-period binomial model.
b) What are the hedge portfolios at t = 1 that help price the call option at that time?
c) Suppose the model price were correct, and the call option were priced in the market at $55. Show how one can make arbitrage profits.
4. Price a call option using the one-period binomial model assuming the following data:
S0 = 129, K=80, U=1.5, D=0.5 and R=1.1. What does the replicating portfolio consist of?
5. Use the data from problem 5, compute the put price and validate the put-call parity.