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.
Author(s) Details:
Gerald W. Buetow Jr.,
BFRC Services, LLC, USA.
James Sochacki,
James
Madison University, USA.
Please see the link here: https://stm.bookpi.org/RUMCS-V5/article/view/14216
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