Research On Numerical Methods For Pricing American Call Options On Dividend-paying Stock

Option is one of the core tools of financial derivative security. It plays an important role in the effective management of risk and speculation. The critical thing for the option securities to exist reasonably and develop properly is fair price evaluation. Unlike European options and American call options on non-dividend paying stock, no explicit closed-form formulas have been found for American call options on dividend-paying stock, so approximation methods have to be used in practice. Researching more effective numerical methods able to solve this problem is also important.Numerical methods for pricing the American call options on dividend-paying stock are few, such as the multistep binomial tree method (see [8, 20 and 29]) and finite difference method (see [10, 13, 14, 23 and 26]). However, the first method neglects the possibility of non-fluctuating prices, and computation time is too long; in [23], the explicit difference scheme is short of accuracy and corresponding theoretical analysis. Based on these defects, this thesis considers a non-fluctuating market and presents a corresponding implicit difference scheme for the approximate solution, and adopts the extremun principle to analyze stability and convergence of the scheme. Finally, according to a mixed numerical method for American put options in [24], this thesis combines fast fourier transform and Runge-Kutta method into a new numerical method for American call options on dividend-paying stock.Through analyzing and comparing a series of options, the numerical experiment shows that the methods provided in this thesis all are fast and effective. And the conclusion of"American call options on dividend-paying stock should be exercised in advance"mentioned in [29] is also reached.