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Pricing vulnerable basket spread options with liquidity risk

Author

Listed:
  • Ziming Dong

    (University of International Business and Economics)

  • Dan Tang

    (University of International Business and Economics)

  • Xingchun Wang

    (University of International Business and Economics)

Abstract

In this paper, we investigate the pricing of vulnerable basket options and basket spread options with stochastic liquidity risk. A liquidity-adjusted pricing model is used to incorporate liquidity risk in the market, and the default risk of option issuers is considered as well. An approximation method is applied to derive the closed-form approximated prices, and numerical experiments show that our approximated prices are quite accurate spanning different underlying asset numbers and alternative strike prices. Finally, we illustrate the effects of default risk and liquidity risk on the prices of basket and basket spread options numerically.

Suggested Citation

  • Ziming Dong & Dan Tang & Xingchun Wang, 2023. "Pricing vulnerable basket spread options with liquidity risk," Review of Derivatives Research, Springer, vol. 26(1), pages 23-50, April.
    • Handle: RePEc:kap:revdev:v:26:y:2023:i:1:d:10.1007_s11147-022-09192-0
    DOI: 10.1007/s11147-022-09192-0
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    References listed on IDEAS

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    1. Wang, Xingchun, 2021. "Valuation of options on the maximum of two prices with default risk under GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    2. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    3. U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2008. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 9, pages 185-221, World Scientific Publishing Co. Pte. Ltd..
    4. Pastor, Lubos & Stambaugh, Robert F., 2003. "Liquidity Risk and Expected Stock Returns," Journal of Political Economy, University of Chicago Press, vol. 111(3), pages 642-685, June.
    5. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    6. Petter Bjerksund & Gunnar Stensland, 2014. "Closed form spread option valuation," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1785-1794, October.
    7. 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.
    8. Johnson, Herb & Stulz, Rene, 1987. "The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, vol. 42(2), pages 267-280, June.
    9. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    10. Amihud, Yakov, 2002. "Illiquidity and stock returns: cross-section and time-series effects," Journal of Financial Markets, Elsevier, vol. 5(1), pages 31-56, January.
    11. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 377-389, September.
    12. Chun-Sing Lau & Chi-Fai Lo, 2014. "The pricing of basket-spread options," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1971-1982, November.
    13. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    14. Minqiang Li & Jieyun Zhou & Shi-Jie Deng, 2010. "Multi-asset spread option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 305-324.
    15. Georges Dionne & Geneviève Gauthier & Nadia Ouertani, 2013. "Risk Management of Nonstandard Basket Options with Different Underlying Assets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(4), pages 299-326, April.
    16. Alessio Caldarera & Celso Brunetti, 2005. "Asset Prices and Asset Correlations in Illiquid Markets," 2005 Meeting Papers 288, Society for Economic Dynamics.
    17. Xingchun Wang, 2022. "Pricing European basket warrants with default risk under stochastic volatility models," Applied Economics Letters, Taylor & Francis Journals, vol. 29(3), pages 253-260, February.
    18. Yong Ma & Keshab Shrestha & Weidong Xu, 2017. "Pricing Vulnerable Options with Jump Clustering," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(12), pages 1155-1178, December.
    19. Xingchun Wang & Shiyu Song & Yongjin Wang, 2017. "The Valuation of Power Exchange Options with Counterparty Risk and Jump Risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(5), pages 499-521, May.
    20. Wang, Xingchun, 2022. "Pricing vulnerable options with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    21. 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.
    22. Yung-Ming Shiu & Pai-Lung Chou & Jen-Wen Sheu, 2013. "A closed-form approximation for valuing European basket warrants under credit risk and interest rate risk," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1211-1223, July.
    23. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    24. Geoffrey Poitras, 1998. "Spread options, exchange options, and arithmetic Brownian motion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 18(5), pages 487-517, August.
    25. Shephard, N.G., 1991. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory," Econometric Theory, Cambridge University Press, vol. 7(4), pages 519-529, December.
    26. Dilip B. Madan, 2010. "Conserving Capital by Adjusting Deltas for Gamma in the Presence of Skewness," JRFM, MDPI, vol. 3(1), pages 1-25, December.
    27. 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

    Vulnerable basket spread options; Vulnerable basket options; Stochastic liquidity risk; Default risk;
    All these keywords.

    JEL classification:

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

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