Description
Your program should be written in such a way that there is only one program for each question and all the outputs for each question should be displayed by running the program once only.
- Put down all your observations and outputs of the questions asked in a single Word/LaTeX document. Finally create a pdf
file from the Word/LaTeX file.
- The file names should be your roll numeber and name seprated by “ ”. If your roll number is 100 and your name is xyz then file names should be 100 xyz for output files (in pdf) and 100 xyz q1 and 100 xyz q2 etc for programs. Write your full name and roll number at the top of the output file.
Write a program, using the binomial pricing algorithm, to determine the price of an European call and an European put option (in the binomial model framework) with the following data :
S(0) = 100;K = 105;T = 5;r = 0.05;σ = 0.3.
Take, where , 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).
- Run your program for M = 1,5,10,20,50,100,200,400 to get the initial option prices and tabulate them.
- How do the values of options at time t = 0 compare for various values of M? Compute and plot graphs (of the initial option prices) varying M in steps of 1 and in steps of 5. What do you observe about the convergence of option prices?
- Tabulate the values of the options at t = 0,0.50,1,1.50,3,4.5 for the case M = 20.
Note that your program should check for the no-arbitrage condition of the model before proceeding to compute the prices.
