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%; = 20%:
Use the following two sets of u and d for your program.
(a)
Set 1
: u = e
p
; d = e p
.
t
t
p
+(r
1
2) t ; d = e p
+(r
1
2) t.
(b)
Set 2
: u = e
t
t
2
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):
S(0).
K.
r.
.
M (Do this for three values of K, K = 95; 100; 105).
You may also 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 at least one set (of u; d).
