MA 374 Financial Engineering Lab Lab 02
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 = e
σ
√
∆t
; d = e
−σ
√
∆t
.
(b) Set 2 : u = e
σ
√
∆t+(r− 1
2
σ
2
)∆t
; d = e
−σ
√
∆t+(r− 1
2
σ
2
)∆t
.
Here ∆t =
T
M , 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).
