Comparative Study Of Numerical Methods For American Option Pricing

Option pricing theory is one of financial mathematics and financial engineeringdiscipline research and discussion of hot issues and disciplines forefront. Compared tothe European Option, American Option has a privilege that can be executed inadvance, which has led to greatly increase the difficulty of pricing issues. Analysis ofAmerican option prices constitute a principle to advance the implementation of thestrategy, the optimal implementation of border options nature and focus on resolvinghow to take advantage of the numerical methods for solving option prices as well asthe method of implementation.The main contents are as follows:Chapter1introduced the basic concepts which related financial derivativespricing, development history and Research, also explained the theoretical andpractical significance of the study ofAmerican option pricing.Chapter2gives complete the Black-Scholes model, and draw on a similarapproach to derive the American option pricing model, transaction costs anddividends European and American option pricing model.Chapter3gives several commonly used numerical methods for American optionpricing: the tree diagram method, finite difference method and the finite elementmethod. And ideas borrowed programming gives the details of the calculation processand steps.In Chapter4, the numerical examples is research content, using MATLABsoftware do numerical experiments, analysis of the experimental results andcalculated from convergence, convergence speed, accuracy and stability point of view.Finally, the real price of the stock as the research object, pricing American optionsunder stochastic volatility, and using real stock data to do volatility forecasts, obtainedby the numerical method the price of the option.Analysis Summary and further research are given in Chapter5.