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Pricing holder-extendable call options with mean-reverting stochastic volatility

Ibrahim, SNI and Díaz-Hernández, A and O'Hara, JG and Constantinou, N (2019) 'Pricing holder-extendable call options with mean-reverting stochastic volatility.' ANZIAM Journal, 61 (4). pp. 382-397. ISSN 1446-1811

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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.

Item Type: Article
Uncontrolled Keywords: extendable options; Heston model; fast Fourier transform; finite difference method; Monte Carlo simulation
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 09 Feb 2022 15:11
Last Modified: 18 Aug 2022 12:24
URI: http://repository.essex.ac.uk/id/eprint/32246

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