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A jump-diffusion approach to modelling vulnerable option pricing

Author

Listed:
  • Xu, Weidong
  • Xu, Weijun
  • Li, Hongyi
  • Xiao, Weilin

Abstract

Following the framework of Klein [1996. Journal of Banking and Finance 20, 1211–1229], this paper presents an improved method of pricing vulnerable options under jump diffusion assumptions about the underlying stock prices and firm values which are appropriate in many business situations. In contrast to Klein [1996. Journal of Banking and Finance 20, 1211–1229] model, jumps can be used to model sudden changes in stock prices and firm values. Further, with the jump risk, a firm can default instantaneously because of an unexpected drop in its value. Therefore, our model is able to provide sufficient conceptual insights about the economic mechanism of vulnerable option pricing. The numerical results show that a jump occurrence in firm values can increase the likelihood of default and reduce the vulnerable option prices.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:finlet:v:9:y:2012:i:1:p:48-56
    DOI: 10.1016/j.frl.2011.07.001
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Lihua Zhang & Weiguo Zhang & Weijun Xu & Xiang Shi, 2014. "A Modified Least-Squares Simulation Approach to Value American Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 489-506, December.
    2. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing of vulnerable options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 645-656.
    3. Xingchun Wang, 2020. "Analytical valuation of Asian options with counterparty risk under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(3), pages 410-429, March.
    4. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    5. Gechun Liang & Xingchun Wang, 2021. "Pricing vulnerable options in a hybrid credit risk model driven by Heston–Nandi GARCH processes," Review of Derivatives Research, Springer, vol. 24(1), pages 1-30, April.
    6. Xingchun Wang, 2021. "Pricing vulnerable options with jump risk and liquidity risk," Review of Derivatives Research, Springer, vol. 24(3), pages 243-260, October.
    7. Lian, Yu-Min & Chen, Jun-Home, 2024. "Pricing vulnerable options under cross-asset markov-modulated jump-diffusion dynamics," International Review of Economics & Finance, Elsevier, vol. 94(C).
    8. Min-Ku LEE & Sung-Jin YANG, PhD & Jeong-Hoon KIM, 2017. "Pricing Vulnerable Options with Constant Elasticity of Variance versus Stochastic Elasticity of Variance," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 233-247.
    9. 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).
    10. Wang, Xingchun, 2016. "Pricing vulnerable options with stochastic default barriers," Finance Research Letters, Elsevier, vol. 19(C), pages 305-313.
    11. Wang, Xingchun, 2022. "Pricing vulnerable options with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    12. Chen, Son-Nan & Chiang, Mi-Hsiu & Hsu, Pao-Peng & Li, Chang-Yi, 2014. "Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model," Finance Research Letters, Elsevier, vol. 11(2), pages 161-172.
    13. 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.
    14. 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 options; Jump diffusion model; Discrete time model; Credit risk;
    All these keywords.

    JEL classification:

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

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