JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (3): 22-32.doi: 10.6040/j.issn.1671-9352.0.2024.105

• Financial Mathematics • Previous Articles     Next Articles

Vulnerable European option pricing in a regime-switching and Hawkes jump diffusion model

DU Huiyuan, FAN Xiaoming*   

  1. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan, China
  • Published:2025-03-10

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Abstract: Option pricing with counterparty default risk under stochastic volatility and stochastic interest rate models is studied. In this model, the mean reversion levels of volatility and interest rate process are controlled by a continuous Markov process in a finite state space, and it is assumed that both the underlying asset price process and the counterparty asset price process contain jumps, and their jumps obey the Hawkes process with self-stimulation, and it is assumed that the volatility process also contains jumps. The analytical pricing formula of European vulnerable option is derived by means of measure transform, solution of discount characteristic function and multivariate Fourier transform. Then the fast Fourier transform method is used to calculate the effective approximation of the option analytic pricing formula, and the accuracy of the approximation is verified by Monte Carlo simulation. Finally, the sensitivity of different parameters in the proposed model to the price of vulnerable call options is analyzed, and the difference between the proposed model and the stochastic interest rate model without Markov regime-switching(MRS)is compared by numerical experiments, and the impact of the introduction of regime-switching in the model on the option pricing results is illustrated.

Key words: vulnerable European option, jump clustering, regime-switching, fast Fourier transform

CLC Number: 

  • O211.6
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