Paper: arXiv 2611.00466

Authors: Peter Cotton

Abstract

A regime-switching model lets any parameter of a standard model take a different value in each state of a hidden Markov chain. For the affine and exponential-Lévy models in common use the pricing problem reduces to one linear system, a’ = (Q + diag g(t)) a, with the chain’s generator Q and a model-specific forcing g as its only ingredients. We expand its solution in the mean holding time of the chain to any order, with an initial layer for the starting regime, and identify the first correction as a Green-Kubo matrix from the group inverse of Q. The same system prices bonds, swaptions, caps, credit default swaps, Asian and digital options, and equity options under stochastic rates, with the Gil-Pelaez integrals conditioned on the regime at expiry where a payoff depends on it; barrier, American and Bermudan instruments go to the coupled equations on a grid. Every numerical claim is checked against QuantLib in the limit where the regimes coincide and against an independent referee with switching on, and the implementation is public.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly complex mathematical framework for regime-switching models, deriving an asymptotic expansion for the solution. It demonstrates strong empirical rigor through extensive checks against QuantLib and an independent referee, with public code implementation. The novelty lies in the generalized reduction to a single linear system and the Green-Kubo matrix correction.

Research Flowchart

  flowchart TD
    A[Research Goal: Derivative Pricing with Fast Regime Switches] --> B{Methodology: Regime-Switching Model};
    B --> C{Core Model: Affine & Exponential-Lévy Models};
    C --> D[Computational Process: Solve a' = (Q + diag g(t)) a];
    D --> E[Inputs: Regime-switching chain's generator Q, Model-specific forcing g(t)];
    E --> F[Validation: QuantLib, Independent Referee];
    F --> G[Key Outcomes: Unified Pricing of Bonds, Swaptions, Caps, CDS, Asian, Digital, Equity Options; Public Implementation];