Download Assignment 7 - Introduction to Computational Finance - Fall 2008 | CSCI 6961 and more Assignments Computer Science in PDF only on Docsity! CSCI 6961 RPI Introduction to Computational Finance Fall 2008 ASSIGNMENT 7, due Thursday, November 20 Homeworks are due at the begining of class or in my mail box by 2pm on the due date. The point value for the 6000 level is indicated in small font. 1 (50 (35) points) Price the American Put Option Implement the following three methods for pricing the American Put option. B(S0, K, T, r, σ, N) : Use the Binomial model with N discretization steps - use the risk neutral probability. LSM(S0, K, T, r, σ, N, M, L) : Use the LSM algorithm with N discretization steps and M paths to obtain the exercise thresholds, doing regression with second order polynomials, and then use another L paths to price the option. OPT (S0, K, T, r, σ, N, M, L) : Use N discretization steps and M paths to obtain the exercise thresholds. To get the thresholds, do not use regression, but use the algorithm to obtain the optimal threshold as discussed in class. Then use another L paths to price the option. Test your algorithm: I computed B(10, 9, 1, 0.04, 0.5, N) for N ∈ {102, 103, 104, 105} and obtained {1.26369, 1.26590, 1.26558, 1.26554}. In the rest of this homework, set S0 = 10, K = 10, T = 2, r = 0.05; σ = 0.2, and for the Monte Carlo approaches, use the continuous model for generating the paths. (a) For N ∈ {100, 1000}, obtain B(S0, K, T, r, σ, N). (b) For (N, M, L) ∈ {(50, 10000, 10000), (100, 5000, 5000), (50, 5000, 50000)}, obtain LSM(S0, K, T, r, σ, N, M, L). Compare the runtimes and accuracy. (c) For (N, M, L) as in the previous part, obtain OPT (S0, K, T, r, σ, N, M, L). Compare the runtimes and accuracy. (d) Suppose that you did not use new paths to compute the price, but the same paths on which you got the exercise thresholds. Compute OPT (S0, K, T, r, σ, 50) using 50 paths in this way. Repeat this many times, and take the average. Now compute OPT (S0, K, T, r, σ, 50, 50, 50) many times and take the average. Explain your results. 1
