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MA374 Lab 3 Solved

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.

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