Paper: arXiv 2610.20366

Authors: Karl Kristian Engelund

Abstract

Regime-switching multi-factor models are widely used in quantitative finance, but filtering does not by itself determine when an agent should act on inferred regime changes. We formulate online regime detection with latent factors and hidden regimes as a Bayesian decision problem balancing false alarms, detection delay, and misclassification. Since posterior regime probabilities are generally non-Markovian, the problem is represented as a measure-valued optimal stopping problem and approximated using particle filtering with Monte Carlo dynamic programming. A single-change-point Heston model provides a benchmark. With observed variance, the problem reduces to a two-dimensional Markov free-boundary problem, while under latent variance decisions are based on the filtered posterior measure. Numerical experiments in Heston and regime-switching Vasicek models show that the latent-information procedure can outperform feasible plug-in rules.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical and rigorous approach to a novel problem in quantitative finance. The combination of Bayesian decision theory, optimal stopping, and particle filtering is sophisticated, and the numerical experiments provide solid empirical backing for the proposed methodology. The work is well-structured and clearly articulated, making a significant contribution to the field.

Research Flowchart

  flowchart TD
    A[Research Goal: Online Regime Detection in Latent Factor Models] --> B{Methodology: Bayesian Decision Problem};
    B --> C[Approach: Measure-valued Optimal Stopping];
    C --> D{Approximation: Particle Filtering & Monte Carlo DP};
    D --> E[Models/Data: Heston, Vasicek, Latent Factors];
    E --> F[Outcomes: Outperformance of Latent-Information Procedure];

Cited References (69)

  1. Optimal stopping and free-boundary problems (2006)
  2. Global $C^1$ Regularity of the Value Function in Optimal Stopping Problems (2020)
  3. Realised volatility and parametric estimation of Heston SDEs (2020)
  4. Optimal stopping rules (2008)
  5. Real-time sequential detection for diffusion signals (1987)
  6. Bayesian online changepoint detection (2007) — link
  7. Online learning of order flow and market impact with Bayesian change-point detection methods — → 2307.02375
  8. Bayesian quickest detection in sensor arrays (2012)
and 61 more
  1. Multiple model bootstrap filter for maneuvering target tracking (2000)
  2. Parameter learning and change detection using a particle filter with accelerated adaptation (2021)
  3. Differentiable interacting multiple model particle filtering (2026)
  4. Solving high-dimensional optimal stopping problems using deep learning (2021)
  5. The Gapeev–Shiryaev Conjecture (2026)
  6. Quickest Detection Problems for Bessel Processes (2017)
  7. Bayesian quickest detection problems for some diffusion processes (2013)
  8. Quickest Detection Problems for Ornstein–Uhlenbeck Processes (2024)
  9. Changes of structure in financial time series and the GARCH model (2004)
  10. Filtering of Stochastic Volatility Model (2003)
  11. Fundamentals of Stochastic Filtering (2009)
  12. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle (1989)
  13. A regime-switching Heston model for VIX and S&P 500 implied volatilities (2014)
  14. Regime-switching stochastic volatility model: estimation and calibration to VIX options (2017)
  15. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  16. How important is the correlation between returns and volatility in a stochastic volatility model? Empirical evidence from pricing and hedging in the S&P 500 index options market (1998)
  17. A yield-factor model of interest rates (1996)
  18. Specification analysis of affine term structure models (2000)
  19. Option valuation using the fast Fourier transform (1999)
  20. Transform analysis and asset pricing for affine jump-diffusions (2000)
  21. The jump-risk premia implicit in options: Evidence from an integrated time-series study (2002)
  22. Joint pricing of VIX and SPX options with stochastic volatility and jump models (2015)
  23. Long swings in the dollar: are they in the data and do markets know it (1990)
  24. Modeling the conditional distribution of interest rates as a regime-switching process (1996)
  25. Option pricing under regime switching (2002)
  26. Option valuation and hedging strategies with jumps in the volatility of asset returns (1993)
  27. Hidden Markov models and applications (2022)
  28. Option pricing and Esscher transform under regime switching (2005)
  29. Pricing volatility swaps under Heston’s stochastic volatility model with regime switching (2007)
  30. Maximum likelihood estimation of stochastic volatility models (2007)
  31. Simulation-based sequential analysis of Markov switching stochastic volatility models (2007)
  32. A Regime-Switching Model of the Yield Curve at the Zero Bound (2013)
  33. Kalman filtering of generalized Vasicek term structure models (1999)
  34. Estimation of state-space models with endogenous Markov regime-switching parameters (2014)
  35. An equilibrium characterization of the term structure (1977)
  36. The pricing of options and corporate liabilities (1973)
  37. Analytical pricing of American put options on a zero coupon bond in the Heath–Jarrow–Morton model (2015)
  38. Optimal stopping of a Hilbert space valued diffusion: an infinite dimensional variational inequality (2016)
  39. A Tutorial on Particle Filtering and Smoothing: Fifteen Years Later (2011)
  40. Unspanned stochastic volatility and the pricing of commodity derivatives (2009)
  41. Do prices reveal the presence of informed trading? (2015)
  42. Arithmetic Models for Oil Futures, Vanilla, and Calendar Spread Options (2026)
  43. On Optimum Methods in Quickest Detection Problems (1963)
  44. Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (2006)
  45. Sequential testing problems for Bessel processes (2018)
  46. The Bayesian choice: from decision-theoretic foundations to computational implementation (2007)
  47. The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes (1958)
  48. A Markov model for switching regressions (1973)
  49. Threshold models in non-linear time series analysis (1983)
  50. Pricing currency options under two-factor Markov-modulated stochastic volatility models (2008)
  51. On Markov‐modulated Exponential‐affine Bond Price Formulae (2009)
  52. Market price of risk specifications for affine models: Theory and evidence (2007)
  53. Monotonicity and robustness in Wiener disorder detection (2019)
  54. Continuity of the optimal stopping boundary for two-dimensional diffusions (2019)
  55. An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options (2013)
  56. The interacting multiple model algorithm for systems with Markovian switching coefficients (1988)
  57. A simulation approach to optimal stopping under partial information (2009)
  58. Quarticity and other functionals of volatility: Efficient estimation (2013)
  59. Numerical Solution of Stochastic Differential Equations (1992)
  60. Invariant Measures and Euler–Maruyama’s Approximations of State-Dependent Regime-Switching Diffusions (2018)
  61. American option pricing and filtering with a hidden regime-switching jump diffusion (2022)

1 of 69 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.