MA 374 Financial Engineering Lab Lab 03
1. Write a program to determine the initial price of the lookback (European) option in the binomial model, using
the basic binomial algorithm (used in earlier lab assignments), with the following data:
S(0) = 100; T = 1; r = 8%; σ = 20%.
The payoff of the lookback option is given by
V = max
0≤i≤M
S(i) − S(M),
where S(i) = S(i∆t) with ∆t =
T
M (M being the number of subintervals of the time interval [0, T]). Use the
continuous compounding convention in your calculations (i.e., both in p˜ and in the pricing formula). Use the
following values of u and d for your program:
u = e
σ
√
∆t+(r− 1
2
σ
2
)∆t
; d = e
−σ
√
∆t+(r− 1
2
σ
2
)∆t
(a) Obtain the initial price of the option for M = 5, 10, 25, 50.
(b) How do the values of options at time t = 0 compare for the above values of M that you have taken ?
(c) Tabulate the values of the options at all intermediate time points for M = 5.
2. Repeat Problem 1 using a (Markov based) computationally efficient binomial algorithm. Make a comparative
analysis of the two algorithms, like computational time, the value of M it can handle, etc.
3. As in Problem 2, use a (Markov based) computationally efficient binomial algorithm to price an European call
option. Make a comparative analysis of the two algorithms, like computational time, the value of M it can
handle, etc.
