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

Paper: arXiv 2605.03082

Authors: Lorenzo Mercuri, Andrea Perchiazzo, Edit Rroji, Ilaria Stefano

Abstract

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a highly novel mathematical concept (Time to Transition) grounded in stochastic diffusions, exact Gaussian bridge likelihoods, and infill asymptotics. While the theoretical model and inference framework are rigorous and mathematically sophisticated, empirical validation on extensive real-world market datasets remains limited in the summary.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Infer Market-Implied Time to Transition (TtT) from Greenium Term Structure"] --> B["Inputs:<br>Cross-Maturity Greenium Yield Differences"]
    
    subgraph Methodology & Computation
        B --> C["Stochastic Framework:<br>Regulatory Deadline & Regime-Switching Models"]
        C --> D["Inference Engine:<br>Gaussian Bridge Likelihood & Filtering Recursions"]
        D --> E["Theoretical Analysis:<br>Fixed-Horizon Infill Asymptotics"]
    end

    E --> F["Outcomes:<br>1. Operational daily tool to monitor TtT<br>2. Structural identification of regime-wise parameters"]

Cited References (102)

1. Green bond finance and certification (2017)
2. Classical Potential Theory and Its Probabilistic Counterpart (1984)
3. Conditional Brownian motion (1957) — link
4. Trading algorithms with learning in latent alpha models (2019)
5. Continuous-Time Markov Chains: An Applications-Oriented Approach (1991) — link
6. A tutorial on hidden M arkov models and selected applications in speech recognition (1989) — link
7. M arkov Processes: Characterization and Convergence (1986)
8. Asymptotic Statistics (1998)

1 of 102 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.