Fast Fourier Transform Based Computation of American Options under Economic Recession Induced Volatility Uncertainty

Abstract

The menace of Economic recession to uncertainty in the payoff of investments and standard of living cannot be over emphasized. This paper presents fast Fourier transform method for the valuation of American style options under the exposure of Economic recession. A multi-factor affine Exponential jump model with Recession induced Stochastic volatility and Intensity, which is a partial Integro-Differential Equation (PIDE) is presented. We show how to determine the characteristic function of the model via generating function. A close form characteristic formula for a financial claim satisfying the PIDE in pricing both European style and American style options in Fourier based transform was done. A numerical based Fourier transform algorithm FFT for European call option valuation was extended to the model under study. The algorithm was further extended to American call options valuation by adding premium price to the European call options price. Numerical result was presented to reflect the effect of economic recession induced volatility on options prices and that of the usual volatility. The result shows some significant vicissitudes in the options values in the two states of the Economy. The result output indicated that the model is effective and reliable compared to other existing models. The fast Fourier transform (FFT) approach gave better option value and compared to both Black-Scholes Merton (BSM) and American Option solver as shown in the table under numerical result section. We used Nigerian Flourmill Stock (NFS) prices for data calibration and reported the stock performance during the first Nigerian recession and recovery year in the Appendix section.