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

Part of: Mathematical finance

Published online by Cambridge University Press:  14 October 2019

S. N. I. IBRAHIM Open the ORCID record for S. N. I. IBRAHIM [Opens in a new window] ,
A. DÍAZ-HERNÁNDEZ Open the ORCID record for A. DÍAZ-HERNÁNDEZ [Opens in a new window] ,
J. G. O’HARA Open the ORCID record for J. G. O’HARA [Opens in a new window]  and
N. CONSTANTINOU
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
*
✉iqmal@upm.edu.my
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Abstract

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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.

Keywords

extendable optionsHeston modelfast Fourier transformfinite difference methodMonte Carlo simulation

MSC classification

Primary: 91G60: Numerical methods (including Monte Carlo methods)
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 4 , October 2019 , pp. 382 - 397
Copyright
© 2019 Australian Mathematical Society

Footnotes

*

Deceased.

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