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. The latter paper illustrates the construction of several risk-neutral measures circumventing this drawback so as to yield path-independent pricing. The current paper aims at improving on the work of Godin et al. (2019) by providing additional risk-neutral measures which also purge path-dependence, but which do not share some disadvantages associated with measures from the latter paper. Risk-neutral measures derived in the current work are based on the Extended Girsanov Principle (EGP). 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. Another notable extension provided by our work versus Godin et al. (2019) is the incorporation of non-Gaussian distributions for log-returns. Numerical experiments show that incorporating such non-Gaussian distributions along with regime unobservability aversion within the EGP-based pricing procedures provides additional flexibility allowing controlling the level, skew, depth and curvature of implied volatility surfaces generated by the pricing model. Moreover, Monte-Carlo simulations provide evidence that the pricing of variable annuities is more influenced by the underlying asset return distributions than the choice of risk-neutral measure.