Market-implied time to transition to a low-carbon economy

In the transition to a low-carbon economy, the difference in greenium between twin bonds with different maturities is expected to vanish, or at least to decline in both level and volatility. This motivates the introduction of stochastic models for the greenium term-structure slope subject to a terminal transition constraint. Empirically, this slope exhibits mean-reverting behavior together with substantial changes across volatility regimes. To capture these features, we introduce two related models.

The first one is a Regulatory Deadline-Constrained Model (RDCM), namely a linear mean-reverting diffusion with a deterministic terminal date at which the greenium difference is forced to vanish. The second is a Switching Regulatory Deadline-Constrained Model (SRDCM), where the perceived transition deadline is regime-dependent and evolves according to a discrete-time latent Markov structure. In both cases, the model is formulated so that the transition date affects not only the terminal condition, but also the pre-terminal behavior of the drift target and diffusion coefficient through the time remaining to transition.

For the RDCM, we derive the exact Gaussian bridge likelihood and study its calibration on fixed observation grids. We then show that, under a fixed-horizon infill asymptotic scheme, the diffusion block can be consistently identified on the part of the observation interval where it is asymptotically visible. This result yields a structurally grounded local temporal discrimination rule between competing transition labels in the switching framework. The models are calibrated using data from twin German government bonds. In the empirical analysis, the evidence suggests that, in the most recent period, market perception has shifted toward a slower transition path and a delayed convergence of the greenium term structure.