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;σ = 0.3.
Take, where , 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.
