Pricing Formula for European Option in Regime-Switching Mixed Fractional Brownian Motion Model with Jumps

In this paper, we deal with a new combination of regime-switching model and mixed fractional Brownian motion model with jumps (MFBMJ hereafter) to capture more precisely underlying asset behaviors. The former represents stochastic volatility and heavy tails, while the latter expresses abnormal phenomena such as long-range dependence, self-similarity and jumps. When an underlying asset process follows a regime-switching MFBMJ model (“RS” for simplicity hereafter), explicit pricing formulae for European options were derived. Finally, some numerical experiments and empirical applications imply that our “RS” model is some improvement in comparison with the others.