Introduction To The Pricing Methods Of American Option And Their Comparison

The first chapter is the introduction,which is the definition and classification of options and option pricing theory basis, which introduced the principle of risk-neutral, arbitrage pricing theory and option value analysis, the option at the end of this chapter pricing theory from scratch, from simple to complex development process to do a lot of presentations, from generation to generation of experts and scholars have made outstanding contributions to this end.Especially the contribution made by Black and Scholes, introduced in Chapter Ⅱ the assumptions of the Black-Scholes model, to establish the process and the derivation of the pricing formula, and review the work of Black and Scholes, on the other hand, we also found that the shortcomings of the Black-Scholes model:only applies to European options, but this study is the American option, but even so, our work is not useless, in the next chapter we highlight the American option pricing model, the first clear description of the problem of American option pricing in a free boundary problem, we have established the characteristics of the American option pricing model of the two forms:parabolic equation model and the variational inequality equation model. The last one in this chapter, we introduced the American option pricing bullish-bearish symmetrical relationship.Model is not also need solving method For this reason, in the next fourth, fifth and sixth chapters, respectively, introduced the American option of three solutions: the finite difference method, the binomial tree method, least squares Monte Carlo simulation method.The finite difference method is the first difference method, and then based on the discrete variational inequality model derivation, shows the difference schemes and implicit difference scheme, which shows the differential format also gives the Matlab program, as well as a numerical cases, the final evaluation of the differential method. Chapter of the binomial tree method first introduce the definition of the binary tree methods, and then given a binary tree of the pricing process, according to the characteristics of American options pricing American options. Finally, the method of evaluation, this chapter belong to the contents of an introductory character, because the choice of parameter uncertainty in the binomial tree method, several outstanding experts and scholars were given the same parameter selection methods in previous studies, only specific conditions analysis, coupled with the "dimension effect" of the binomial tree method, the application is very limited, this article only do these presentations.Least squares Monte Carlo method is the recent emergence of new, not original, but very new application is also very convenient and widely put it joined a detailed description of Matlab programming.also carried out numerical experiments Finally, the method of evaluation.Done so much work, the structure of this thesis is:options, the BS model, the model of American option, American option pricing method for solving it.