A closed-form pricing formula for European options under a new three-factor stochastic volatility model with regime switching

In this paper, a new stochastic volatility model is proposed for European option pricing with the long-term mean divided into two parts; one is controlled by a stochastic process, while another is governed by a Markov chain to incorporate the regime-switching mechanics. The advantage of adopting this new model is that there exists a closed-form solution for European option prices based on the characteristic function of the underlying price, which could save a lot of effort when it is applied in real markets. The influence of introducing regime switching into option pricing models is particularly studied with numerical experiments, and results show that the regime switching could cause quite a big difference.