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

Traditional pricing methods for derivatives pricing under regime-switching frameworks produce path-dependent prices for vanilla options when regimes are latent. The current paper provides a risk-neutral measure based on the Extended Girsanov Principle (EGP) which purges such path-dependence. 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. 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.