Binomial and continuous model - mathematics of finance, Finance Basics

Consider a binomial model of a risky asset with the parameters r = 0:06, u = 0:059, d = 0:0562, S0 = 100, T = 1, 4t = 1=12. Note that u and d are monthly effective rates of return and r is the annual effective risk-free interest rate.

(1) Determine the price of a European put option with strike price X = 98 on the above non-dividend paying asset at time 0 and find x(1); y(1), i.e., the number of shares of the stock and risk-free asset needed at time 0 to replicate the European option over the first time-step.

(2) Compute the Black-Scholes price of a European put option with the above specifications and report the relative error between the price obtained in (1) and the Black-Scholes price, i.e., compute,

2489_Binomial and Continuous Model.png

compute x(1); y(1), i.e., the number of shares of the stock and risk-free asset needed at time 0 to instantaneously delta hedge the European put option. Compare x(1); y(1) with the values computed in part (1).

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