A refracted process in options: A credit valuation application

Abstract

Borrowing from the principle of refraction in optics, we develop an option pricing model in which the underlying asset’s process changes upon touching a barrier, alongside a structural credit risk model. To achieve this, we extend the Black–Scholes and Merton models to incorporate regime shifts when a barrier is crossed. Our credit model demonstrates that if a drop in firm value below a certain threshold triggers a structural change in its policies — that in our framework is captured by a shift in the model governing its time evolution — this affects the initial value of its loans. As the policy change alters the underlying asset process, loan values decrease, and credit spreads widen. Our findings underscore the importance of accounting for regime shifts and their impact on loan pricing in dynamic market conditions.