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Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate

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  • BEN-ZHANG YANG

    (School of Mathematics, Sichuan University, Chengdu, P. R. China)

  • JIA YUE

    (School of Economic Mathematics, South Western University of Finance and Economics, Chengdu, P. R. China)

  • NAN-JING HUANG

    (School of Mathematics, Sichuan University, Chengdu, P. R. China)

Abstract

This paper focuses on the pricing of variance swaps in incomplete markets where the short rate of interest is determined by a Cox–Ingersoll–Ross model and the stock price is determined by a Heston model with simultaneous Lévy jumps. We obtain the pricing kernel and the equivalent martingale measure in an equilibrium framework. We also give new closed-form solutions for the delivery prices of discretely sampled variance swaps under the forward measure, as opposed to the risk neural measure, by employing the joint moment generating function of underlying processes. Theoretical results and numerical examples are provided to illustrate how the values of variance swaps depend on the jump risks and stochastic interest rate.

Suggested Citation

  • Ben-Zhang Yang & Jia Yue & Nan-Jing Huang, 2019. "Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-33, June.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:04:n:s021902491950016x
    DOI: 10.1142/S021902491950016X
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    2. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Continuous time mean-variance-utility portfolio problem and its equilibrium strategy," Papers 2005.06782, arXiv.org, revised Nov 2020.
    3. Xin‐Jiang He & Sha Lin, 2023. "Analytically pricing European options under a hybrid stochastic volatility and interest rate model with a general correlation structure," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 951-967, July.
    4. Xu, De-xuan & Yang, Ben-zhang & Kang, Jian-hao & Huang, Nan-jing, 2021. "Variance and volatility swaps valuations with the stochastic liquidity risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    5. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Mean-variance-utility portfolio selection with time and state dependent risk aversion," Papers 2007.06510, arXiv.org, revised Aug 2020.

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