Comparison of Numerical Methods to Value European and American Put Options.

The aim of this dissertation is to investigate and analyse various numerical methods with implementation techniques in order to determine the quick and accurate models that can be used in option pricing. The numerical approaches are able to produce accurate prices for both European and American options. The European options have correct value that was formulated by Black, Scholes and Merton. However, their analytic model fails to solve American put option which is the continuing inspiration for researchers to develop new approaches or figure out the best combination of existing models. This paper tests 5 binomial trees, WAND technique, Monte Carlo simulation, Adaptive Mesh Model, Crank-Nicolson and Hopscotch models. Our findings indicate that the acceleration techniques increase efficiency of models successfully. Richardson extrapolation is exceptionally useful for the binomial models which enjoy monotonic and smooth convergence features. We also conclude that Leisen-Reimer tree with truncation outperforms other numerical models for European options. Tian Flexible and Leisen-Reimer with truncation and extrapolation are the best methods to value American options