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Pricing vulnerable spread options with liquidity risk under Lévy processes

Author

Listed:
  • Cai, Chengyou
  • Wang, Xingchun
  • Yu, Baimin
Abstract
In this paper, we consider vulnerable spread options with stochastic liquidity risk. Lévy processes are introduced to characterize jumps and we allow the liquidity discount factor to be related to a mean-reversion process. Through bivariate Fourier transforms, we successfully get the approximated pricing formula in the proposed model, and numerical experiments show that the approximated prices are very accurate. We finally focus on the impact of asymmetric jump risk and stochastic liquidity risk on vulnerable spread option prices.

Suggested Citation

  • Cai, Chengyou & Wang, Xingchun & Yu, Baimin, 2024. "Pricing vulnerable spread options with liquidity risk under Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).
    • Handle: RePEc:eee:ecofin:v:72:y:2024:i:c:s1062940824000494
    DOI: 10.1016/j.najef.2024.102124
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    References listed on IDEAS

    as
    1. Acharya, Viral V. & Pedersen, Lasse Heje, 2005. "Asset pricing with liquidity risk," Journal of Financial Economics, Elsevier, vol. 77(2), pages 375-410, August.
    2. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    3. Puneet Pasricha & Song-Ping Zhu & Xin-Jiang He, 2022. "A closed-form pricing formula for European options in an illiquid asset market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-18, December.
    4. Alessio Caldarera & Celso Brunetti, 2005. "Asset Prices and Asset Correlations in Illiquid Markets," 2005 Meeting Papers 288, Society for Economic Dynamics.
    5. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    6. Zhiguo He & Konstantin Milbradt, 2014. "Endogenous Liquidity and Defaultable Bonds," Econometrica, Econometric Society, vol. 82(4), pages 1443-1508, July.
    7. Xu, Weidong & Xu, Weijun & Li, Hongyi & Xiao, Weilin, 2012. "A jump-diffusion approach to modelling vulnerable option pricing," Finance Research Letters, Elsevier, vol. 9(1), pages 48-56.
    8. Arora, Navneet & Gandhi, Priyank & Longstaff, Francis A., 2012. "Counterparty credit risk and the credit default swap market," Journal of Financial Economics, Elsevier, vol. 103(2), pages 280-293.
    9. Justin Chircop & Michele Fabrizi & Antonio Parbonetti, 2018. "The impact of the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005 repo ‘safe harbor’ provisions on investors," The European Journal of Finance, Taylor & Francis Journals, vol. 24(18), pages 1772-1798, December.
    10. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    11. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2018. "Illiquidity Premia in the Equity Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 811-851.
    12. Xingchun Wang, 2021. "Pricing vulnerable options with jump risk and liquidity risk," Review of Derivatives Research, Springer, vol. 24(3), pages 243-260, October.
    13. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    14. Petter Bjerksund & Gunnar Stensland, 2014. "Closed form spread option valuation," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1785-1794, October.
    15. Huawei Niu & Dingcheng Wang, 2016. "Pricing vulnerable options with correlated jump-diffusion processes depending on various states of the economy," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1129-1145, July.
    16. Wang, Xingchun, 2022. "Pricing vulnerable options with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    17. 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).
    18. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    19. Lihui Tian & Guanying Wang & Xingchun Wang & Yongjin Wang, 2014. "Pricing Vulnerable Options with Correlated Credit Risk Under Jump‐Diffusion Processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(10), pages 957-979, October.
    20. Zelei Li & Dan Tang & Xingchun Wang, 2023. "Valuing basket-spread options with default risk under Hawkes jump-diffusion processes," The European Journal of Finance, Taylor & Francis Journals, vol. 29(12), pages 1406-1431, August.
    21. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
    22. Mao‐Wei Hung & Yu‐Hong Liu, 2005. "Pricing vulnerable options in incomplete markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(2), pages 135-170, February.
    23. Xin‐Jiang He & Sha Lin, 2023. "Analytically pricing exchange options with stochastic liquidity and regime switching," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(5), pages 662-676, May.
    24. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    25. Laura Ballotta & Ioannis Kyriakou, 2014. "Monte Carlo Simulation of the CGMY Process and Option Pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1095-1121, December.
    26. Guanying Wang & Xingchun Wang & Xinjian Shao, 2020. "The valuation of vulnerable European options with risky collateral," The European Journal of Finance, Taylor & Francis Journals, vol. 26(13), pages 1315-1331, July.
    27. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    28. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2016. "The importance of stock liquidity on option pricing," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 457-467.
    29. Hull, John & White, Alan, 1995. "The impact of default risk on the prices of options and other derivative securities," Journal of Banking & Finance, Elsevier, vol. 19(2), pages 299-322, May.
    30. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    31. Li, Zelei & Wang, Xingchun, 2020. "Valuing spread options with counterparty risk and jump risk," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
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    More about this item

    Keywords

    Stochastic liquidity risk; Mean-reversion processes; Lévy processes; Default risk;
    All these keywords.

    JEL classification:

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

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