Write a program to determine the initial price of an American call and an American 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 set of u and d for your program:
p p
u = e t+(r 12 2) t ; d = e t+(r 12 2) t:
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, plot the initial prices of both call and put options 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).
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%; = 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 t = MT (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:
p
+(r
1
2) t
p
+(r
1
2) t
u = e
t
;
d = e
t
2
2
Obtain the initial price of the option for M = 5; 10; 25; 50.
How do the values of options at time t = 0 compare for the above values of M that you have taken ?
Tabulate the values of the options at all intermediate time points for M = 5.
Repeat Problem 2 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.
As in Problem 3, 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.
