An American Option Pricing Model With Historical Price Constraints Based On Linear Complementarity

With the continuously development in financial market all over the world,the financial trading system and all kinds of financial instruments have been advancing,and various financial derivatives have been created and used. The pricing of derivative securities, particularly options, have aroused people’s long-term concern, and itself has been a widely studied problem in financial mathematics. American option’s buyer can exercise in advance, so it is more popular than European option. On the other hand, this freedom of exercise time makes the pricing process much more complex. At present, the problem of American option pricing, especially American put option, is still a challenge in the field of derivative securities pricing.In the thesis, we study an optimization model of American option pricing. Firstly, under the assumption of no-arbitrage, Black-Scholes model is revised as a stochastic complementarity problem, and then we derive a linear complementarity model by using the finite difference approximation on it. Furthermore this linear complementarity model we obtain can be transformed into an optimization model. At last, in consideration of the influence of historical data, we add two different constraints according to historical option prices to improve the model and give two optimization methods for the problem. We give two different forms of objective function to solve the problem. Numerical results show the usefulness and rationality of the proposed model.The thesis is arranged as follows:In Chapter1, we give the introduction of option, the property of option pricing, Black-Scholes option pricing model, expansion of Black-Scholes model, and several classical numerical methods for option pricing.In Chapter2, we introduce complementarity problem, including the concept,forms and several algorithms.In Chapter3, we give the free boundary of American option pricing, the deduction of the linear complementarity model of American option pricing and its application to more complex American options. In Chapter4, an American option pricing optimization model with historical price constraints is presented, we also give two different methods for improving according historical price constraints.In Chapter5, we give algorithms to solve the problem we presented in Chapter4. In account of the property of objective functions,we choose two different algorithms,followed with their processes, respectively.In Chapter6,we give our experiment results. We experiment with several share options in HKSE(Hong Kong Stock Exchange, and the result show the rationality of our model.Conclusion part is the summary of the thesis.