Calibrating an option pricing model under regime-switching volatility

Abstract: A Black-Scholes market is considered in which asset prices are modelled by a geometric Brownian motion with regime-switching volatility. The regime-switching allows the volatility to jump randomly amongst a finite number of volatility states. Pricing equations of European options are derived and the equations are solved numerically. The model is calibrated for two, three and four volatility states to observed market prices of call options on the OMXS30 index during the period August 2003 to August 2006. The findings show that two volatility states are sufficient to replicate market prices with a high degree of accuracy. Mispricings are found to be considerably smaller under a regime-switching model than under the traditional Black-Scholes model.