Regime recovery using implied volatility in Markov modulated market model

Abstract

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 theoretical price of European vanilla options. By pretending these prices or their numerical approximations as traded prices, we have first computed the implied volatility (IV) of the underlying asset. Then by performing several numerical experiments on ternary regime models 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 a particular narrow range, can recover the transition instances of the hidden Markov chain having three states. Such regime recovery for any arbitrary state-space and transition parameters has also been established in a theoretical setting. Moreover, the novel scheme for computing option price is shown to be stable.