Creating a binomial model calculator in matlab

Question

Assignment Instructions:

You are asked to create an American option multiplicative binomial model calculator in MatLab. Both put and call options should be valued. Given u, d, S0, K, r and T (the usual notation applies), you should create an m-file that computes an N-step solution.

You are then asked to also compute the standard hedge sensitivities and comment on their interpretation.

This is an individual assignment. You are asked to make the m-file. Your m-file should contain your name and student ID and your m-file should be populated with sufficient comments that will inform the reader of the code workings.

Terminology:

S: The underlying asset price.

S_T: The underlying asset price at the maturity of the contract.

S_o: The underlying asset price at the start of the contract (at time t₀).

K: The delivery price.

F_to or F_o: The forward price agreed at start of the contract (at time t₀).

FV: The future value of the asset.

P: The present value of the asset.

R: The interest rate.

n: The number of years.

m: The number of compounding periods.

r: The risk-free interest rate.

T: The maturity date of the contract

I: The present value of the known income payment on the underlying asset.

q: The continuous yield on the underlying asset.

U: The present value of the storage costs.

u: The present value of the storage costs expressed as a continuous negative yield.

X: The exercise price on the option.

ITM: in-the-money. When the stock price is greater than the exercise price - i.e. S > X.

ATM: at-the-money. When the stock price is equal to the exercise price - i.e. S = X.

OTM: out-of-the-money. When the stock price is greater than the exercise price - i.e. S > X.

σ: The volatility of the stock price.

c: The call option price.

c_t0: The call option price at the start of the contract (at time t₀).

c_T: The call option price at the maturity of the contract.

p: The put option price.

p_t0: The put option price at the start of the contract (at time t₀).

p_T: The put option price at the maturity of the contract.

u: Proportion of an upward movement.

d: Proportion of an downward movement.

Δ: number of units of the stock.

C_T,u: The call option price at maturity if there was an upward movement in the asset price.

C_T,d: The call option price at maturity if there was an downward movement in the asset price.

p: : The probability of an upward movement.

E[A]: The expected value of A.