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# Refer to the docxAssignment-4Fin 455Spring 2024Due: March 26,

Refer to the docx

Assignment-4

Fin 455

Spring 2024

Due: March 26, 2024

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.

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