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 S(i) − S(M),
0≤i≤M
where S(i) = S(i∆t) with 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:
;
(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.
