IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v245y2015i2p571-580.html
   My bibliography  Save this article

Variance swap with mean reversion, multifactor stochastic volatility and jumps

Author

Listed:
  • Pun, Chi Seng
  • Chung, Shing Fung
  • Wong, Hoi Ying

Abstract

This paper examines variance swap pricing using a model that integrates three major features of financial assets, namely the mean reversion in asset price, multi-factor stochastic volatility (SV) and simultaneous jumps in prices and volatility factors. Closed-form solutions are derived for vanilla variance swaps and gamma swaps while the solutions for corridor variance swaps and conditional variance swaps are expressed in a one-dimensional Fourier integral. The numerical tests confirm that the derived solution is accurate and efficient. Furthermore, empirical studies have shown that multi-factor SV models better capture the implied volatility surface from option data. The empirical results of this paper also show that the additional volatility factor contributes significantly to the price of variance swaps. Hence, the results favor multi-factor SV models for pricing variance swaps consistent with the implied volatility surface.

Suggested Citation

  • Pun, Chi Seng & Chung, Shing Fung & Wong, Hoi Ying, 2015. "Variance swap with mean reversion, multifactor stochastic volatility and jumps," European Journal of Operational Research, Elsevier, vol. 245(2), pages 571-580.
    • Handle: RePEc:eee:ejores:v:245:y:2015:i:2:p:571-580
    DOI: 10.1016/j.ejor.2015.03.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715002337
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.03.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hoi Ying Wong & Jing Zhao, 2010. "Currency option pricing: Mean reversion and multi‐scale stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(10), pages 938-956, October.
    2. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    4. Chung, Shing Fung & Wong, Hoi Ying, 2014. "Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 130-140.
    5. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
    6. Fusai, Gianluca & Marena, Marina & Roncoroni, Andrea, 2008. "Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2033-2045, October.
    7. Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
    8. Gang Li & Chu Zhang, 2010. "On the Number of State Variables in Options Pricing," Management Science, INFORMS, vol. 56(11), pages 2058-2075, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wu, Bin & Chen, Pengzhan & Ye, Wuyi, 2024. "Variance swaps with mean reversion and multi-factor variance," European Journal of Operational Research, Elsevier, vol. 315(1), pages 191-212.
    2. Chiu, Hsin-Yu & Chen, Ting-Fu, 2020. "Impact of volatility jumps in a mean-reverting model: Derivative pricing and empirical evidence," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    3. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    4. Mehrdoust, Farshid & Noorani, Idin & Hamdi, Abdelouahed, 2023. "Two-factor Heston model equipped with regime-switching: American option pricing and model calibration by Levenberg–Marquardt optimization algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 660-678.
    5. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.
    6. Maria Cristina Recchioni & Yu Sun & Gabriele Tedeschi, 2017. "Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1257-1275, August.
    7. Amengual, Dante & Xiu, Dacheng, 2018. "Resolution of policy uncertainty and sudden declines in volatility," Journal of Econometrics, Elsevier, vol. 203(2), pages 297-315.
    8. Kaeck, Andreas & Seeger, Norman J., 2020. "VIX derivatives, hedging and vol-of-vol risk," European Journal of Operational Research, Elsevier, vol. 283(2), pages 767-782.
    9. Aït-Sahalia, Yacine & Amengual, Dante & Manresa, Elena, 2015. "Market-based estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 187(2), pages 418-435.
    10. Recchioni, M.C. & Sun, Y., 2016. "An explicitly solvable Heston model with stochastic interest rate," European Journal of Operational Research, Elsevier, vol. 249(1), pages 359-377.
    11. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    12. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
    13. Chung, Shing Fung & Wong, Hoi Ying, 2014. "Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 130-140.
    14. Lo, Chien-Ling & Shih, Pai-Ta & Wang, Yaw-Huei & Yu, Min-Teh, 2019. "VIX derivatives: Valuation models and empirical evidence," Pacific-Basin Finance Journal, Elsevier, vol. 53(C), pages 1-21.
    15. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    16. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    17. Alfredo Ibáñez, 2008. "The cross-section of average delta-hedge option returns under stochastic volatility," Review of Derivatives Research, Springer, vol. 11(3), pages 205-244, October.
    18. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.
    19. Jacod, Jean & Klüppelberg, Claudia & Müller, Gernot, 2017. "Testing for non-correlation between price and volatility jumps," Journal of Econometrics, Elsevier, vol. 197(2), pages 284-297.
    20. Jaegi Jeon & Geonwoo Kim & Jeonggyu Huh, 2019. "Consistent and Efficient Pricing of SPX and VIX Options under Multiscale Stochastic Volatility," Papers 1909.10187, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:245:y:2015:i:2:p:571-580. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.