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Pricing vulnerable options in incomplete markets

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  • Mao‐Wei Hung
  • Yu‐Hong Liu

Abstract

This paper follows the framework of P. Klein (1996) to price vulnerable options when the market is incomplete. Vulnerable options, which are usually traded in the over‐the‐counter market, may not only face the risk of default but also the risk of illiquidity. Thus, pricing such options under the assumption of market completeness, as was done by H. Johnson and R. Stulz (1987) and P. Klein (1996), seems to be a mistake. Accordingly, the proposed model uses the methodology proposed by J. H. Cochrane and J. Saá‐Requejo (2000) to price vulnerable options under both deterministic and stochastic interest rates in an incomplete market. The model is found to perform well when the interest rate is stochastic. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:135–170, 2005

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jfutmk:v:25:y:2005:i:2:p:135-170
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    Cited by:

    1. Zonggang Ma & Chaoqun Ma & Zhijian Wu, 2022. "Pricing commodity-linked bonds with stochastic convenience yield, interest rate and counterparty credit risk: application of Mellin transform methods," Review of Derivatives Research, Springer, vol. 25(1), pages 47-91, April.
    2. Kim, Donghyun & Kim, Geonwoo & Yoon, Ji-Hun, 2022. "Pricing of vulnerable exchange options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    3. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2017. "Pricing vulnerable options with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 91-103.
    4. Kim, Donghyun & Choi, Sun-Yong & Yoon, Ji-Hun, 2021. "Pricing of vulnerable options under hybrid stochastic and local volatility," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Chang-Chih Chen & Chia-Chien Chang, 2019. "How Big are the Ambiguity-Based Premiums on Mortgage Insurances?," The Journal of Real Estate Finance and Economics, Springer, vol. 58(1), pages 133-157, January.
    6. Sun-Yong Choi & Ji-Hun Yoon & Junkee Jeon, 2019. "Pricing of Fixed-Strike Lookback Options on Assets with Default Risk," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    7. Donghyun Kim & Ji-Hun Yoon, 2023. "Analytic Method for Pricing Vulnerable External Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1561-1591, April.
    8. Chaoqun Ma & Shengjie Yue & Hui Wu & Yong Ma, 2020. "Pricing Vulnerable Options with Stochastic Volatility and Stochastic Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 391-429, August.
    9. Chen, Chang-Chih & Chang, Chia-Chien & Sun, Edward W. & Yu, Min-Teh, 2022. "Optimal decision of dynamic wealth allocation with life insurance for mitigating health risk under market incompleteness," European Journal of Operational Research, Elsevier, vol. 300(2), pages 727-742.
    10. Han, Xingyu, 2018. "Pricing and hedging vulnerable option with funding costs and collateral," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 103-115.
    11. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Sep 2015.
    12. Rafael Company & Vera N. Egorova & Lucas Jódar, 2024. "An ETD Method for Vulnerable American Options," Mathematics, MDPI, vol. 12(4), pages 1-14, February.
    13. 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).
    14. Ban, Mingyuan & Chen, Chang-Chih, 2019. "Ambiguity and capital structure adjustments," International Review of Economics & Finance, Elsevier, vol. 64(C), pages 242-270.
    15. Sun-Yong Choi & Sotheara Veng & Jeong-Hoon Kim & Ji-Hun Yoon, 2022. "A Mellin Transform Approach to the Pricing of Options with Default Risk," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1113-1134, March.
    16. Panhong Cheng & Zhihong Xu & Zexing Dai, 2023. "Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    17. Liang-Chih Liu & Chun-Yuan Chiu & Chuan-Ju Wang & Tian-Shyr Dai & Hao-Han Chang, 2022. "Analytical pricing formulae for vulnerable vanilla and barrier options," Review of Quantitative Finance and Accounting, Springer, vol. 58(1), pages 137-170, January.
    18. 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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