Regime recovery using implied volatility in Markov modulated market model

In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered the locally risk minimizing price of European vanilla options. By pretending these prices or their noisy versions as traded prices, we have first computed the implied volatility (IV) of the underlying asset. Then by performing several numerical experiments we have investigated the dependence of IV on the time to maturity (TTM) and strike price of the vanilla options. We have observed a clear dependence that is at par with the empirically observed stylized facts. Furthermore, we have experimentally validated that IV time series, obtained from contracts with moneyness and TTM varying in particular narrow ranges, can recover the transition instances of the hidden Markov chain. Such regime recovery has also been proved in a theoretical setting. Moreover, the novel scheme for computing option price is shown to be stable.