A Comparative Study of Crank-Nicolson scheme and Monte-Carlo Option Pricing
This study examines the rate of convergence and the accuracy of the two primary option pricing methods used currently by professionals; Monte-Carlo and Crank-Nicolson scheme using the Black-Scholes price as the benchmark price. We also introduce the Antithetic variates to the Monte Carlo, to check how much the technique improves the accuracy of the model. A model that converges faster and is accurate will be important in the valuation of large number of options, this will be beneficial to the current and potential investors dealing with large number of options, usually this is the case in practice. Similarly, by control variates technique, we can use our result to improve the accuracy of pricing options that do not have closed form solution such as American options or other exotic options.