Vulnerable European option pricing in a Markov regime-switching Heston model with stochastic interest rate. (March 2022)

• Record Type: Journal Article
• Authors: Xie, Yurong; Deng, Guohe
• Is Part Of: Chaos, solitons and fractals. Volume 156(2022)
• Publication Date: 2022-03
• Subjects: Vulnerable options -- Regime-switching -- Heston stochastic volatility model -- Stochastic interest rate -- Fast Fourier transform (FFT); G12 -- G13; 60J28 -- 91B25 -- 91G20 -- 91G60; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.111896
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract : highlights: A vulnerable European option under SVSI model with Markov regime-switching is investigated. Analytical expressions of the option price along with its Delta Greek are obtained. We examine the sensitivity analysis of different parameters in our model on option price and Delta value. The fast Fourier transform technique is considered to compute the option price and Delta value. We provide comparison of option price between SVSI model with Markov regime-switching and SVSI model. Abstract: This paper considers pricing of European-style vulnerable options under the Heston stochastic volatility and stochastic interest rate model in which the mean-reversion levels of both variance and interest rate processes are modulated by a continuous-time Markov process with a finite state space. An analytical pricing formula is derived by using the Esscher transform, joint characteristic function and multivariate Fourier transform technique, where the closed-form solution of the characteristic function is obtained by the law of iterated expectation. Then we provide the efficient approximation to calculate the analytical pricing formula of option using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation. Finally, the sensitivity analysis of different parameters in the proposed model on the vulnerable call option price and its Delta value are provided, and the difference between the proposed model and the Heston and stochastic interest rate model with non-Markov regime-switching are presented by some numerical experiments, which shows the influence of introducing regime-switching into Heston model with stochastic interest rate.