Research Of The Approximate Method For American Option Pricing

Options on stocks were first traded in organized exchange in 1973. Since then, there has been a dramatic growth in option market. Now, option business has made in the different exchange all over the word.The development of option trading aroused considerable interest among the academic community. Doctor Black and professor Scholes first gave an option price formula to calculate European Call option. Professor Merton and other scholars extend and complete it. Doctor Black and professor Scholes achieve the Nobel prize because of their contribution in finance domain.Because the American option may early be exercised before the expiration date, its pricing is generally more difficult than that of the European. Traditional method of American option pricing focuses on numerical method. Now there are three kinds of mature numerical methods: they are binomial tree method finite-difference methods and Monte Carlo methods. Overseas and domestic scholars have made thoroughly study on this way and made many mends.However, there aren't analytical formulas for American options, so we cannot get exact solutions and only make an approximation analytical formula. Based of BAW formula, we elicit a new approximation formula. To illustrate the quality and speed of the new method, according to custom, we regard the results gained from the binomial methods with 10000 time steps as the accurate ones, and then compare the original method with ours. Numerical examples show that our algorithm leads to very rapid and accurate results.First, the paper summarizes the origin, development ,meaning and the definition and classification of the option. The classical B-S model and its extending are introduced in chapter two. Chapter three studies the model of American option pricing. Chapter four studies the numerical method of American option. Analytic approximation method is introduced in the chapter five and we make an adjustment of BAW formula. Last we make a tag.