Question: I need help coding the following problem in r. Let S_t be a Geometric Brownian Motion process: S_t = S_0 e^(sigma W_t + (r -
I need help coding the following problem in r.
Let S_t be a Geometric Brownian Motion process: S_t = S_0 e^(sigma W_t + (r - sigma^2/2)t), where r = 0.04, sigma = 0.2, S_0 = $88, W_t is a Standard Brownian Motion process (Standard Wiener process). (a) Estimate the price c of a European Call option on the stock with T = 5, X = $100 by using Monte Carlo simulation. (b) Compute the exact value of the option c by the Black-Scholes formula. Now use variance reduction techniques (whichever you want) to estimate the price in part (a) again. Did the accuracy improve? Comment. Inputs: need Outputs: i. Values: Ca1, Ca2 for part (a); Cb1, Cb2 for part (b) ii. Writeup: comments in a .pdf file for part (b) Let S_t be a Geometric Brownian Motion process: S_t = S_0 e^(sigma W_t + (r - sigma^2/2)t), where r = 0.04, sigma = 0.2, S_0 = $88, W_t is a Standard Brownian Motion process (Standard Wiener process). (a) Estimate the price c of a European Call option on the stock with T = 5, X = $100 by using Monte Carlo simulation. (b) Compute the exact value of the option c by the Black-Scholes formula. Now use variance reduction techniques (whichever you want) to estimate the price in part (a) again. Did the accuracy improve? Comment. Inputs: need Outputs: i. Values: Ca1, Ca2 for part (a); Cb1, Cb2 for part (b) ii. Writeup: comments in a .pdf file for part (b)
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
