Research On The Canonical Distribution, Implementation Of Boundary Parameterization, Dual Analog Algorithm And American Bermudan Option Pricing

In Nineteen seventies, with the collapse of the Bretton Woods system, western countries have abandoned the fixed exchange rate system, began with floating exchange rate system. At the same time, countries also gradually relaxed or abolished supervisin on interest rates and regulatory restrictions on securities market, exchange rate, interest rate and stock price prompted volatility frequently.These encouraged people to need the derivatives market risk aversion function and financial derivatives products to avoild some risk. Although financial derivatives developed among the controversial from the beginning of the birth, even they cause the bankruptcy of Paris bank, financial derivatives have always maintained a rapid development momentum. Even after a sustained rapid development of more than40years, the development of financial derivatives is still be just unfolding. At the beginning of this century, stock options have been launched at the London International Financial Futures Exchange, One Chicago(American Chicago futures exchange, the Chicago Mercantile Exchange and the Chicago Board Options Exchange jointly launched by the exchange), trading volume rose rapidly, at present it has become the world’s first large varieties of futures financial products.Since the option have been after birth, many scholars began to study the option pricing problem. In1973, the two young scholars Black and Scholes the United States of America published "options and corporate liabilities pricing" in the famous "political economics" journals, put forward the famous Black-Scholes model. The analytical solutions calculated European option, has exerted a great influence on the academic and practical circles. Since then, scholars all over the world bengan to modify the defect of the model,and explore improvement and expansion. The same year, Professor Merton of Harvard University published a paper about options,introducing all aspects of the option pricing from another angle. The BS model has greatly promoted the development of the option market. With the rapid development of the option market, more and more people began to study option pricing, many scholars put forward different pricing model. In general, the option pricing model can be divided into continuous-time model and the discrete-time model, pricing results can also be divided into analytic solution and numerical solution. The BS model is analytical solution,but numerical methods, such as Monte Carlo simulation, two forks tree and finite difference method are discrete time models, whose solution is the numerical.According to the American option and Bermuda option,the present paper focuses on the combination of regular distribution, implementation of boundary parameterization, dual analog algorithm, to price American option and Bermudan option, based on the summary of the existing options research methods.on the basis of previous studies, the preent paper proposes a called regular exercise boundary parametric dual simulation method (canonical exercise-boundary-parameterization primal-dual-simulation, CEP) on the American Bermudan option pricing. The method is divided into three parts:first, risk neutral distribution from the historical data of a certain period of regularization method (risk-neutral distribution), then to get the random samples from the distribution of returns, which simulate the risk neutral path. Secondly, using the Least Squares Monte Carlo (Monte Carlo) method to obtain the option price bounds from the path (Lower Bounds) and the optimal exercise boundary. Finally, in the lower bound and the optimal exercise boundary based on the obtained simulation method, using the dual bound (Upper Bounds),which is the final price of spot right.Among the results,volatility is one of the most important parameters in the modern option pricing theory, but we can not access from the capital market directly. Stutzer (1996,2000) proposed a regular pricing method (canonical valuation method) successfully to circumvent the volatility estimation problem or the underlying assumptions about assets movement process,got the success of the European option pricing. The so-called regular pricing, refers to obtain the risk neutral probability of the return rate corresponding from the time series of price, then the expectation and the discount, so as to obtain the European option price. The method has the advantages, which does not need to care about the distribution of the underlying asset price, and estimating the volatility.