Paper: arXiv 2412.04589

Authors: Martin Larsson, Shukun Long

Abstract

Markovian projections arise in problems where we aim to mimic the one-dimensional marginal laws of an Itô semimartingale by using another Itô process with Markovian dynamics. In applications, Markovian projections are useful in calibrating jump-diffusion models with both local and stochastic features, leading to the study of the inversion problems. In this paper, we invert the Markovian projections for pure jump processes, which can be used to construct calibrated local stochastic intensity (LSI) models for credit risk applications. Such models are jump process analogues of the notoriously hard to construct local stochastic volatility (LSV) models used in equity modeling.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using advanced measure-theoretic probability, semimartingale theory, and filtration analysis to invert Markovian projections for pure jump processes. However, it is purely theoretical and completely lacks empirical backtesting, numerical implementations, or financial datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Construct calibrated LSI models by inverting Markovian projections for pure jump processes] --> B[Inputs: 1D marginal laws of Itô semimartingale & Target Markovian dynamics]
    B --> C[Methodology: Formulate inversion of Markovian projection for pure jump processes]
    C --> D[Computational Process: Compute state-dependent jump intensities & calibrate to market inputs]
    D --> E[Outcomes: Successful construction of Local Stochastic Intensity models for credit risk]

Cited References (6)

  1. Mimicking the marginal distributions of a semimartingale (2012) — link
  2. Interest rate modeling. volume 3: products and risk management (2010)
  3. Pricing with a smile (1994)
  4. Non–regular M cKean– V lasov equations and calibration problem in local stochastic volatility models (2024) — link
  5. Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives (2005)
  6. Denseness of adapted processes among causal couplings (2020) — link

0 of 6 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.