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Covariance And Correlation Swaps For Financial Markets With Markov-Modulated Volatilities

Author

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  • GIOVANNI SALVI

    (Department of Methods and Models for Economics Territory and Finance MEMOTEF, 'Sapienza' University of Rome, Via del Castro Laurenziano, 9, Rome, 00161, Italy)

  • ANATOLIY V. SWISHCHUK

    (Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada)

Abstract

In this paper, we price covariance and correlation swaps for financial markets with Markov-modulated volatilities. As an example, we consider stochastic volatility driven by a two-state continuous Markov chain. In this case, numerical examples are presented for VIX and VXN volatility indices (S&P 500 and NASDAQ-100, from January 2004 to June 2012). We also use VIX (January 2004 to June 2012) to price variance and volatility swaps for the two-state Markov-modulated volatility, and we present a numerical result in this case.

Suggested Citation

  • Giovanni Salvi & Anatoliy V. Swishchuk, 2014. "Covariance And Correlation Swaps For Financial Markets With Markov-Modulated Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-23.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:01:n:s021902491450006x
    DOI: 10.1142/S021902491450006X
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    References listed on IDEAS

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    1. José Da Fonseca & Martino Grasselli & Florian Ielpo, 2011. "Hedging (Co)Variance Risk With Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 899-943.
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    Cited by:

    1. Semere Habtemicael & Indranil SenGupta, 2016. "Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-35, December.
    2. Anatoliy Swishchuk & Sebastian Franco, 2023. "Pricing of Averaged Variance, Volatility, Covariance and Correlation Swaps with Semi-Markov Volatilities," Risks, MDPI, vol. 11(9), pages 1-22, September.
    3. Nicholas Salmon & Indranil SenGupta, 2021. "Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging," Papers 2105.02325, arXiv.org.
    4. Escobar, Marcos & Fang, Lin, 2020. "Stochastic volatility models for the implied correlation index," Finance Research Letters, Elsevier, vol. 35(C).
    5. Xin-Jiang He & Song-Ping Zhu, 2019. "Variance And Volatility Swaps Under A Two-Factor Stochastic Volatility Model With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-19, June.
    6. Nicholas Salmon & Indranil SenGupta, 2021. "Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging," Annals of Finance, Springer, vol. 17(4), pages 529-558, December.
    7. 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).

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