Pricing and hedging for correlation options with regime switching and common jump risk

Abstract

This article investigates the pricing of the correlation options under regime switching models with common jump risk. We assume that the values of model parameters are modulated by a continuous-time, finite-state, observable Markov chain which is used to describe the states of an economy. In addition, the common jump reflects the correlated jump risk between the underlying assets. According to the Fourier transform method, we first derive the semi-analytical pricing formula for the correlation options. Then, some hedging strategies such as Greek letters and minimum variance hedging strategies are offered. Finally, we provide numerical examples to illustrate the effects of the regime switching and the common jump risk on the correlation option price by using the fast Fourier transform (FFT) algorithm.

Keywords:

• Correlation option
• regime switching
• common jump risk
• fast Fourier transform (FFT)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Here, it is also feasible to start from the real world probability measure. In this case, we must choose an equivalent martingale measure for pricing derivatives since there are infinitely many equivalent martingale measures in an incomplete market. According to different criteria, many equivalent martingale measures can be obtained, such as the minimum variance martingale measure, the Esscher transform measure, the minimum entropy martingale measure and so on. In particular, regime switching Esscher transform is the most commonly used method for selecting an equivalent martingale measure in a regime switching market. To get more details about regime switching Esscher transform for two jump-diffusion processes with correlated jumps, one can refer to Niu and Wang (2016).

Additional information

Funding

This work was supported by the Philosophy and Social Science Research in Colleges and Universities of Jiangsu Province (2021SJA0362), the Humanity and Social Science Youth Foundation of the Ministry of Education of China (18YJC910012), Open project of Jiangsu key laboratory of financial engineering (NSK2021-13, NSK2021-15), Natural Science Foundation of the Jiangsu Higher Education Institutions (19KJB110003).