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AN IMEX-BASED APPROACH FOR THE PRICING OF EQUITY WARRANTS UNDER FRACTIONAL BROWNIAN MOTION MODELS

Part of: Applications General and miscellaneous specific topics

Published online by Cambridge University Press:  23 August 2023

WENTING CHEN Open the ORCID record for WENTING CHEN [Opens in a new window]  and
XIAOYING JIANG
WENTING CHEN
Affiliation:
Department of Business, Jiangnan University, Wuxi 214100, Jiangsu, China; e-mail: wtchen@jiangnan.edu.cn
XIAOYING JIANG*
Affiliation:
Department of Mathematics, Zhejiang A&F University, Hangzhou 310027, China; e-mail: jxy@zafu.edu.cn
*
e-mail: cwtwx@163.com
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Abstract

In this paper, the pricing of equity warrants under a class of fractional Brownian motion models is investigated numerically. By establishing a new nonlinear partial differential equation (PDE) system governing the price in terms of the observable stock price, we solve the pricing system effectively by a robust implicit-explicit numerical method. This is fundamentally different from the documented methods, which first solve the price with respect to the firm value analytically, by assuming that the volatility of the firm is constant, and then compute the price with respect to the stock price and estimate the firm volatility numerically. It is shown that the proposed method is stable in the maximum-norm sense. Furthermore, a sharp theoretical error estimate for the current method is provided, which is also verified numerically. Numerical examples suggest that the current method is efficient and can produce results that are, overall, closer to real market prices than other existing approaches. A great advantage of the current method is that it can be extended easily to price equity warrants under other complicated models.

Keywords

equity warrantsGMFBM modelnonlinear PDEIMEX methoderror analysisupwind scheme

MSC classification

Primary: 00A69: General applied mathematics
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 64 , Issue 4 , October 2022 , pp. 380 - 393
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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