Calculate of the price of a call option by binomial tree models and compare the results with the theoretical Black-Scholes formula.
Strike price = $120;
Expiration time = 1 year;
Annual interest rate = 0.05;
Stock volatility = 0.35.
For the initial stock price, S0 = 100.45
1. Find the price of the call option by the Black-Scholes formula rounded to the nearest cent.
2. Experiment with the number of steps for the binomial tree model until your numerical result stabilizes to within one cent of the result given by the Black-Scholes formula.
3. Submission of files (e.g., spreadsheets) of the binomial stock price and option price trees for binomial tree approximations in increments of steps no more than 50. For example, if a 200 step binomial tree is needed to approximate to within one cent of the price given by the Black-Scholes formula, you need to submit at least the data for four binomial trees of 50, 100, 150, and 200 steps. For each number of steps, indicate the parameters (R, u, d, p ) you have used to construct the trees.
Please include where appropriate:
(a) The theoretical computation by the Black-Scholes formula;
(b) Brief explanation of the theoretic basis for binomial tree approximations to Black-Scholes formula;
(c) A summary of your numerical calculations (numbers of steps used, scaled parameters, successive approximate call prices).
Black-Scholes Formulas are examined.