## 01 Apr Assignment-4 Fin 455

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.