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Pricing Fade-in Options Under GARCH-Jump Processes

Author

Listed:
  • Xingchun Wang

    (University of International Business and Economics)

  • Han Zhang

    (Renmin University of China)

Abstract

In this paper, we investigate fade-in options under GARCH-jump processes. Specifically, we adopt NIG distributions to capture jump risk, and both market and individual jumps are considered. In the pricing model driven by GARCH-jump processes, we obtain the prices of fade-in options using the Fourier transform methods. Finally, we use the derived pricing formulae to illustrate the effects of fade-in sets and the parameters in the jump processes.

Suggested Citation

  • Xingchun Wang & Han Zhang, 2024. "Pricing Fade-in Options Under GARCH-Jump Processes," Computational Economics, Springer;Society for Computational Economics, vol. 64(4), pages 2563-2584, October.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:4:d:10.1007_s10614-023-10527-8
    DOI: 10.1007/s10614-023-10527-8
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    References listed on IDEAS

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    1. Susanne Griebsch & Uwe Wystup, 2011. "On the valuation of fader and discrete barrier options in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 693-709.
    2. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    3. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    4. Jean-François Bégin & Christian Dorion & Geneviève Gauthier, 2020. "Idiosyncratic Jump Risk Matters: Evidence from Equity Returns and Options," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 155-211.
    5. Wang, Xingchun & Zhang, Han, 2022. "Pricing basket spread options with default risk under Heston–Nandi GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    8. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
    9. Bing-Huei Lin & Mao-Wei Hung & Jr-Yan Wang & Ping-Da Wu, 2013. "A lattice model for option pricing under GARCH-jump processes," Review of Derivatives Research, Springer, vol. 16(3), pages 295-329, October.
    10. Wang, Xingchun, 2020. "Valuation of Asian options with default risk under GARCH models," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 27-40.
    11. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, vol. 54(1), pages 377-402, February.
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    13. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
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    More about this item

    Keywords

    GARCH-jump processes; Fade-in options; Fourier transform; Default risk;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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