Regime Switching Rough Heston Model

Abstract

The regime switching rough Heston model has two important features on different time scales. The regime switching is motivated by changes in the long term behaviour. The parameter of the model might change over time due to macro-economic reasons. Therefore we introduce a Markov chain to model the switches in the long term mean of the volatility. The rough behaviour is a more local property and is motivated by the stylized fact that volatility is less regular than a standard Brownian motion. Therefore the driving noise in the model is a fractional Brownian motion. We derive and implement pricing formulae for call and put option and then add some insights into the effects of the rough behaviour and the regime switches to these prices. The techniques are much more involved than for the standard Heston model, since the rough processes do neither have the Markov property nor the semi-martingale property. The regime switches introduce as an additional complexity time inhomegeneity.