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PRICING HOLDER-EXTENDABLE CALL OPTIONS WITH MEAN-REVERTING STOCHASTIC VOLATILITY

Published online by Cambridge University Press:  14 October 2019

S. N. I. IBRAHIM
Affiliation:
Department of Mathematics, Faculty of Science and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia email iqmal@upm.edu.my
A. DÍAZ-HERNÁNDEZ
Affiliation:
Faculty of Economics and Business, Universidad Anahuac Mexico-Norte, Huixquilucan 52786, Mexico email adan.diaz@anahuac.mx
J. G. O’HARA
Affiliation:
School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK email johara@essex.ac.uk
Corresponding

Abstract

Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carlo simulation, and we determine the efficiency and accuracy of the Fourier method in pricing holder-extendable call options for Heston parameters calibrated from the subprime crisis. We show that the fast Fourier transform reduces the computational time required to produce a range of holder-extendable call option prices by at least an order of magnitude. Numerical results also demonstrate that when the Heston correlation is negative, the Black–Scholes model under-prices in-the-money and over-prices out-of-the-money holder-extendable call options compared with the Heston model, which is analogous to the behaviour for vanilla calls.

Type
Research Article
Copyright
© 2019 Australian Mathematical Society

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Deceased.

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