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 t_{0}).
K: The delivery price.
F_{to} or F_{o}: The forward price agreed at start of the contract (at time t_{0}).
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 t_{0}).
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 t_{0}).
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.