1. Write a program to determine the initial price of an European call and an European put option in the binomial model with the following data :
S(0) = 100;K = 100;T = 1;M = 100;r = 8%;σ = 20%.
Use the following two sets of u and d for your program.
√ √
(a) Set 1 : u = eσ ∆t ; d = e−σ ∆t.
(b) Set 2 : .
Here ∆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).
Now, carry out a sensitivity analysis of the initial price as follows: Plot the initial prices of both call and put options (for both the above sets of u and d) by varying one of the parameters at a time (as given below) while keeping the other parameters fixed (as given above):
(a) S(0).
(b) K.
(c) r.
(d) σ.
(e) M (Do this for three values of K, K = 95,100,105).
Please do plots in 3-D also (by considering two parameters at a time).
2. Now take any path-dependent derivative of your choice and do the above exercise for both set of (u,d).
