Multiscale stochastic elasticity of variance for options and equity linked annuity; A Mellin transform approach

It is important to impose a persistent stochastic factor on the underlying asset model to obtain the fair value of financial derivatives with long time-to-maturities. Our empirical study, including the Covid-19 pandemic crisis period, indicates the presence of both fast and slow-scale in the elasticity of variance of S&P 500. This paper extends the elasticity in terms of multiscale stochastic process and obtains a closed form analytic pricing formula for European options and then derive the fair value of Equity-Linked-Annuity (ELA). The Mellin transform method for solving the relevant partial differential equations provides a computationally-efficient pricing formula for the options and the ELA. The prices can be easily calculated simply by taking derivatives of the Black-Scholes option price. Our results reveal the sensitivity of the ELA term structure to the fast-scale or slow-scale related group parameters. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.