Market-implied time to transition to a low-carbon economy: a stochastic modelling and inference framework

This paper introduces a new market-implied object, Time to Transition (TtT), extracted from the difference between two selected nodes of the greenium term structure. TtT is defined as the latent waiting time until this cross-maturity greenium difference vanishes, meaning that the greenium becomes equal across the two selected maturities. We develop an inference theory for this object. To model TtT, we introduce two tractable stochastic frameworks: the Regulatory Deadline-Constrained Model, in which the transition date is fixed, and a switching extension, in which alternative transition dates capture heterogeneous perceived deadlines across economic agents. The paper combines two layers of analysis. On a fixed daily grid, a deadline-constrained diffusion provides a tractable benchmark through an exact Gaussian bridge likelihood, while the switching extension preserves tractability through regime-specific bridge densities and filtering recursions. Under a fixed-horizon infill scheme, the same framework yields a structural identification result for the regime-wise diffusion parameters, with full or partial consistency depending on the observed region. The paper therefore contributes both a new inferential object, market-implied transition timing based on cross-maturity differences in the greenium term structure, and a two-layer inference framework: finite-sample filtering provides an operational monitoring tool, while fixed-horizon infill asymptotics specify when the regime-wise diffusion parameters carrying information about competing transition dates can be consistently estimated.