Approximating Option Prices Using the Power Series Method

Abstract

The Power Series Method (PSM) is used as the numerical framework for estimating the Black-Scholes partial differential equation. The Black-Scholes model is a powerful tool for valuation of equity options. The Black-Scholes model is used to calculate the theoretical price of European put and call options, ignoring any dividends paid during the option’s lifetime. PSM offers several advantages over traditional finite difference methods. The PSM is more stable than explicit methods and thus computationally more efficient. It is as accurate as hybrid approaches like Crank Nicolson and faster to compute. It is more accurate over a far wider spectrum of time steps. Finally, and importantly, it can be expressed analytically thus offering the capability of performing comparative statics in a far more stable and accurate environment. For more complex application this last advantage may have wide implications in producing hedge ratios for synthetic replication purposes. This study concludes that PSM is an excellent alternative to the numerical finance literature.