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Calibration and hedging under jump diffusion

Author

Listed:
  • C. He
  • J. Kennedy
  • T. Coleman
  • P. Forsyth
  • Y. Li
  • K. Vetzal

Abstract

A jump diffusion model coupled with a local volatility function has been suggested by Andersen and Andreasen (2000). By generating a set of option prices assuming a jump diffusion with known parameters, we investigate two crucial challenges intrinsic to this type of model: calibration of parameters and hedging of jump risk. Even though the estimation problem is ill-posed, our results suggest that the model can be calibrated with sufficient accuracy. Two different strategies are explored for hedging jump risk: a semi-static approach and a dynamic technique. Simulation experiments indicate that each of these methods can sharply reduce risk exposure. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • C. He & J. Kennedy & T. Coleman & P. Forsyth & Y. Li & K. Vetzal, 2006. "Calibration and hedging under jump diffusion," Review of Derivatives Research, Springer, vol. 9(1), pages 1-35, January.
    • Handle: RePEc:kap:revdev:v:9:y:2006:i:1:p:1-35
    DOI: 10.1007/s11147-006-9003-1
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    References listed on IDEAS

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    Cited by:

    1. van der Zwaard, Thomas & Grzelak, Lech A. & Oosterlee, Cornelis W., 2021. "A computational approach to hedging Credit Valuation Adjustment in a jump-diffusion setting," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Olivier Le Courtois & François Quittard-Pinon & Xiaoshan Su, 2020. "Pricing and hedging defaultable participating contracts with regime switching and jump risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 303-339, June.
    3. Kuo-Shing Chen & Yu-Chuan Huang, 2021. "Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging," Mathematics, MDPI, vol. 9(20), pages 1-24, October.
    4. Ke Nian & Thomas F. Coleman & Yuying Li, 2018. "Learning minimum variance discrete hedging directly from the market," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1115-1128, July.
    5. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
    6. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    7. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Pricing and hedging contingent claims using variance and higher order moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 531-550, April.
    8. Hilliard, Jimmy E. & Hilliard, Jitka, 2019. "A jump-diffusion model for pricing and hedging with margined options: An application to Brent crude oil contracts," Journal of Banking & Finance, Elsevier, vol. 98(C), pages 137-155.
    9. PeiLin Hsieh & QinQin Zhang & Yajun Wang, 2018. "Jump risk and option liquidity in an incomplete market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(11), pages 1334-1369, November.
    10. Nian, Ke & Coleman, Thomas F & Li, Yuying, 2021. "Learning sequential option hedging models from market data," Journal of Banking & Finance, Elsevier, vol. 133(C).
    11. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
    12. Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2016. "American-style options in jump-diffusion models: estimation and evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1313-1324, August.
    13. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
    14. Luo, Rui & Fortenbery, T. Randall, 2016. "Corporate Hedging In Incomplete Markets: A Solution Under Price Transmission," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235444, Agricultural and Applied Economics Association.
    15. Konstantinos Skindilias & Chia Lo, 2015. "Local volatility calibration during turbulent periods," Review of Quantitative Finance and Accounting, Springer, vol. 44(3), pages 425-444, April.
    16. Yangang Chen & Justin W. L. Wan, 2019. "Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions," Papers 1909.11532, arXiv.org.
    17. Thomas Coleman & Yuying Li & Cheng Wang, 2013. "Stable local volatility function calibration using spline kernel," Computational Optimization and Applications, Springer, vol. 55(3), pages 675-702, July.
    18. J. S. Kennedy & P. A. Forsyth & K. R. Vetzal, 2009. "Dynamic Hedging Under Jump Diffusion with Transaction Costs," Operations Research, INFORMS, vol. 57(3), pages 541-559, June.
    19. Liuren Wu & Jingyi Zhu, 2017. "Simple Robust Hedging with Nearby Contracts," Journal of Financial Econometrics, Oxford University Press, vol. 15(1), pages 1-35.

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