Consider a model for a security with time zero value S0 = 150, a yearly effectiv

Question

Consider a model for a security with time zero value S0 = 150, a yearly effective interest rate of .01% and volatility ^2 = (.02)^2 . Implement a binomial model to price option in python.

2. Price an American Put Option with expiry T = 1/4, T = 1/2 , T = 3/4 and T = 1 years and strike price X = 150. Carry out the binomial model in N = 50, N = 100 and N = 500 steps. Repeat with an interest rate of r = .02% Compare the values calculated with the value of the perpetual American Put.

For all problems, plot V (St , t) for t = i/12, for i = 1, 2, ... That is, plot the monthly value of the option as a function of the current stock price – and compare with the corresponding closed form solution.

(just need help with the last part with the plotting in python)

Explanation / Answer

Here, u=1.25 and d = 0.80, X=60,

Node A

Option Price = S - X where S is the price of the stock

= 60 - 50 = 10

Node B

S = 50*1.25 = 62.5; since this price is greater than X, option price = 0

Node C

S = 50*0.8 = 40

Value of put = 60 - 40 = 20

Node D

S = 50*1.25*1.25

Again the option expires worthless

Node E

S = 50*1.25*0.8 = 50

Option value = 60 - 50 = 10

Node F

S = 50*0.8*0.8 = 32

Option value = 60 - 32 = 28

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