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Pricing vulnerable options with correlated jump-diffusion processes depending on various states of the economy

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  • Huawei Niu
  • Dingcheng Wang

Abstract

In this paper, we use a Markov-modulated regime switching approach to model various states of the economy, and study the pricing of vulnerable European options when the dynamics of the underlying asset value and the asset value of the counterparty follow two correlated jump-diffusion processes under regime switching. The correlation is modelled by both the diffusion parts and the pure jump parts which describe the uncertainty of the value of the risky assets. We develop a method to determine an equivalent martingale measure and a parsimonious representation of the risk-neutral density is provided. Based on this, we derive an analytical pricing formula for vulnerable options via two-dimensional Laplace transforms, and implement the formula through numerical Laplace inversion.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:7:p:1129-1145
    DOI: 10.1080/14697688.2015.1090623
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    Citations

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    Cited by:

    1. Wang, Guanying & Wang, Xingchun & Shao, Xinjian, 2022. "Exchange options for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    2. 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.
    3. Junkee Jeon & Geonwoo Kim, 2023. "Valuation of Commodity-Linked Bond with Stochastic Convenience Yield, Stochastic Volatility, and Credit Risk in an Intensity-Based Model," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    4. Huang, Shoude & Guo, Xunxiang, 2022. "Valuation of European-style vulnerable options under the non-affine stochastic volatility and double exponential jump," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. 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, March.
    6. F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "CVA and vulnerable options pricing by correlation expansions," Annals of Operations Research, Springer, vol. 299(1), pages 401-427, April.
    7. Xingchun Wang, 2021. "Pricing vulnerable options with jump risk and liquidity risk," Review of Derivatives Research, Springer, vol. 24(3), pages 243-260, October.
    8. 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).
    9. Xiangdong Liu & Zanbin Zhang, 2023. "Pricing European Vulnerable Options with Jumps and Stochastic Default Obstacles Barrier under Regime Switching," Mathematics, MDPI, vol. 11(19), pages 1-18, October.
    10. Wang, Xingchun, 2022. "Pricing vulnerable options with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).

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