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A lattice approach for option pricing under a regime-switching GARCH-jump model

Published online by Cambridge University Press:  29 July 2021

Zhiyu Guo Open the ORCID record for Zhiyu Guo [Opens in a new window]  and
Yizhou Bai Open the ORCID record for Yizhou Bai [Opens in a new window]
Zhiyu Guo
Affiliation:
Business School, Nankai University, Tianjin 300071, China. E-mail: [email protected]
Yizhou Bai
Affiliation:
College of Science, Civil Aviation University of China, Tianjin 300071, China. E-mail: [email protected]
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Abstract

In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

Keywords

GARCH processJumpLattice algorithmOption pricingRegime switching
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 4 , October 2022 , pp. 1138 - 1170
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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