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OPTION PRICING UNDER THE KOBOL MODEL

Part of: Parabolic equations and systems Applications

Published online by Cambridge University Press:  12 September 2018

WENTING CHEN  and
SHA LIN Open the ORCID record for SHA LIN [Opens in a new window]
WENTING CHEN
Affiliation:
School of Business, Jiangnan University, Wuxi, Jiangsu Province, China email cwtwx@163.com
SHA LIN*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email sl945@uowmail.edu.au
*
✉sl945@uowmail.edu.au
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Abstract

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We consider the pricing of European options under a modified Black–Scholes equation having fractional derivatives in the “spatial” (price) variable. To be specific, the underlying price is assumed to follow a geometric Koponen–Boyarchenko–Levendorski process. This pure jump Lévy process could better capture the real behaviour of market data. Despite many difficulties caused by the “globalness” of the fractional derivatives, we derive an explicit closed-form analytical solution by solving the fractional partial differential equation analytically, using the Fourier transform technique. Based on the newly derived formula, we also examine, in theory, many basic properties of the option price under the current model. On the other hand, for practical purposes, we impose a reliable implementation method for the current formula so that it can be easily used in the trading market. With the numerical results, the impact of different parameters on the option price are also investigated.

Keywords

option pricingfractional derivativeKoBol processfractional partial differential equation

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 35K25: Higher-order parabolic equations
Type
Research Article
Information
The ANZIAM Journal , Volume 60 , Issue 2 , October 2018 , pp. 175 - 190
Copyright
© 2018 Australian Mathematical Society 

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