Fourier Transform of Stock Asset Returns Uncertainty under Covid-19 Surge

Abstract

This study presents  Fourier Transform of  Stock asset returns uncertainty under Covid-19 surge.    Computational  issue   with respect to Covid-19 induced payoff uncertainty of option on an underlying stock  is mathematically studied. A newly modified Black-Scholes model (MBSM) is proposed incorporating Factorial function for  generalization of Black-Scholes model (BSM) and random variable volatility function as an alternative to constant volatility in  the (BSM).  A closed form integral formula for stock price is obtained for MBSM. The variable volatility function is to account for uncertainty effect owing to Covid-19 on the stock price in the MBSM. Option prices are compared based on the selected methods. The option output via the MBSM and Fast Fourier transform (FFT) method varies on replicating simulation which is more realistic in financial market compared to the BSM which returns constant option price all-through. Hence, the study findings show that the  MBSM  assumption of non-constancy in the volatility term suits the  stock markets behaviour  over the  BSM.