Write a program, using the binomial pricing algorithm, to determine the price of an European call and an European put option (in the binomial model framework) with the following data :
S(0) = 100; K = 105; T = 5; r = 0:05; = 0:3:
p
Take u = e t+(r 12 2) t and d = e 12 2) t, where t = MT , with M being the number of subintervals
in the time interval [0; T ]. Use the continuous compounding convention in your calculations (i.e., both in p~ and in the pricing formula).
Run your program for M = 1; 5; 10; 20; 50; 100; 200; 400 to get the initial option prices and tabulate them.
How do the values of options at time t = 0 compare for various values of M? Compute and plot graphs (of the initial option prices) varying M in steps of 1 and in steps of 5. What do you observe about the convergence of option prices?
Tabulate the values of the options at t = 0; 0:50; 1; 1:50; 3; 4:5 for the case M = 20.
Note that your program should check for the no-arbitrage condition of the model before proceeding to compute the prices.
