Option Pricing in Regime-Switching Frameworks With the Extended Girsanov Principle

The recent work of Godin et al. (2019) on derivatives pricing under regime-switching frameworks highlights that traditional pricing methods produce path-dependent prices for vanilla options when regimes are latent. Since such a feature is deemed inconvenient, the latter paper provides the construction of several risk-neutral measures circumventing this problem so as to yield path-independent pricing. The current paper aims at complementing the work of Godin et al. (2019) by providing the construction of an additional risk-neutral measure based on the Extended Girsanov Principle (EGP) which also purges the path-dependence effect. The advantage of the EGP approach lies in its implementation simplicity and its clear interpretability in terms of consistency with hedging agents locally minimizing their risk-adjusted discounted squared hedging errors