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Hedging of options in presence of jump clustering

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  • Hainaut, Donatien
  • Moraux, Franck

Abstract

This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor's 500.
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Suggested Citation

  • Hainaut, Donatien & Moraux, Franck, 2018. "Hedging of options in presence of jump clustering," LIDAM Reprints ISBA 2018037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2018037
    Note: In : The Journal of Computational Finance, vol. 22, no. 3, p. 1-35 (2018)
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    Cited by:

    1. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.
    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. Brignone, Riccardo & Gonzato, Luca & Lütkebohmert, Eva, 2023. "Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants," Journal of Banking & Finance, Elsevier, vol. 148(C).
    4. Leunga Njike, Charles Guy & Hainaut, Donatien, 2024. "Affine Heston model style with self-exciting jumps and long memory," LIDAM Discussion Papers ISBA 2024001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Song, Shiyu, 2024. "The valuation of arithmetic Asian options with mean reversion and jump clustering," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    6. Charles Guy Njike Leunga & Donatien Hainaut, 2024. "Affine Heston model style with self-exciting jumps and long memory," Annals of Finance, Springer, vol. 20(1), pages 1-43, March.
    7. Riccardo Brignone & Carlo Sgarra, 2020. "Asian options pricing in Hawkes-type jump-diffusion models," Annals of Finance, Springer, vol. 16(1), pages 101-119, March.
    8. Hui Qu & Tianyang Wang & Peng Shangguan & Mengying He, 2024. "Revisiting the puzzle of jumps in volatility forecasting: The new insights of high‐frequency jump intensity," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(2), pages 218-251, February.
    9. Jean-David Fermanian, 2020. "On the Dependence between Default Risk and Recovery Rates in Structural Models," Annals of Economics and Statistics, GENES, issue 140, pages 45-82.
    10. Njike Leunga, Charles G. & Hainaut, Donatien, 2022. "Long memory self-exciting jump diffusion for asset prices modeling," LIDAM Discussion Papers ISBA 2022003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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