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LOCALLY RISK-MINIMIZING HEDGING FOR EUROPEAN CONTINGENT CLAIMS WRITTEN ON NON-TRADABLE ASSETS WITH COMMON JUMP RISK

Published online by Cambridge University Press:  01 March 2021

Xiaonan Su ,
Yu Xing ,
Wei Wang Open the ORCID record for Wei Wang [Opens in a new window]  and
Wensheng Wang
Xiaonan Su
Affiliation:
School of Statistics and Mathematics, Nanjing Audit University, Nanjing, China
Yu Xing
Affiliation:
School of Finance, Nanjing Audit University, Nanjing, China
Wei Wang
Affiliation:
School of Mathematics and Statistics, Ningbo University, Ningbo, China E-mail: wangwei2@nbu.edu.cn
Wensheng Wang
Affiliation:
School of Economics, Hangzhou Dianzi University, Hangzhou, China
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Abstract

This article investigates the optimal hedging problem of the European contingent claims written on non-tradable assets. We assume that the risky assets satisfy jump diffusion models with a common jump process which reflects the correlated jump risk. The non-tradable asset and jump risk lead to an incomplete financial market. Hence, the cross-hedging method will be used to reduce the potential risk of the contingent claims seller. First, we obtain an explicit closed-form solution for the locally risk-minimizing hedging strategies of the European contingent claims by using the Föllmer–Schweizer decomposition. Then, we consider the hedging for a European call option as a special case. The value of the European call option under the minimal martingale measure is derived by the Fourier transform method. Next, some semi-closed solution formulae of the locally risk-minimizing hedging strategies for the European call option are obtained. Finally, some numerical examples are provided to illustrate the sensitivities of the optimal hedging strategies. By comparing the optimal hedging strategies when the underlying asset is a non-tradable asset or a tradable asset, we find that the liquidity risk has a significant impact on the optimal hedging strategies.

Keywords

common jump riskhedging strategylocal risk minimizationnon-tradable assets
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 581 - 605
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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