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EQUILIBRIUM VALUATION OF CURRENCY OPTIONS UNDER A DISCONTINUOUS MODEL WITH CO-JUMPS

Published online by Cambridge University Press:  20 January 2020

Yu Xing Open the ORCID record for Yu Xing [Opens in a new window] ,
Yuhua Xu  and
Huawei Niu Open the ORCID record for Huawei Niu [Opens in a new window]
Yu Xing
Affiliation:
School of Finance, Nanjing Audit University, Nanjing 211815, China; Jiangsu Key Laboratory of Financial Engineering (Nanjing Audit University), Nanjing 211815, China E-mail: xingyu5901@hotmail.com
Yuhua Xu
Affiliation:
School of Finance, Nanjing Audit University, Nanjing 211815, China
Huawei Niu
Affiliation:
School of Finance, Nanjing Audit University, Nanjing 211815, China
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Abstract

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

Keywords

co-jumpcurrency optionequilibrium valuationpartial integro-differential equation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 432 - 450
Copyright
© Cambridge University Press 2020

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