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Let h=T/N be the length of one time-step in the binomial tree model. Set u=exp(h)andd=exp(h). Fix T=1,=0.2,S(0)=K=50 and interest rate of r=5% yearly, compounded continuously.
Let h=T/N be the length of one time-step in the binomial tree model. Set u=exp(h)andd=exp(h). Fix T=1,=0.2,S(0)=K=50 and interest rate of r=5% yearly, compounded continuously. There are no dividends. 1. Compute the price C(0,S0) of a European Call with the above parameters using N=4,8,15,30,60,100,150 (i.e. varying the number of steps, while keeping the maturity fixed and using the particular scaling of u and d above. Note that as N grows, h shrinks.) 2. Also compute the Black-Scholes price of this Call CBS(0,S0). Comment on the answer in relation to what you obtained in part 1. 3. Repeat the above for the Call Delta, i.e. compute the initial Delta of the Call using the binomial tree and N=4,8,15,30,60,100,150, and compare to the Black-Scholes BS(0,S0)
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