Journal of Mathematics and Modeling in Finance

Volatility Regimes and Tail Behavior in EUR/USD Returns: A Parsimonious Two-Stage Markov-Switching and Quantile Regression Approach

Articles in Press

Document Type : Research Article

Author

Forough Esmaeily-Sadrabadi

Assistant Professor of Economics, Department of Economics, Faculty of Humanities & Social Sciences, Ardakan University, Ardakan, Iran

10.22054/jmmf.2026.91756.1268
Abstract
This study provides a complementary empirical analysis of daily EUR/USD log-returns using a two-stage framework that combines a two-state Markov-Switching volatility model with quantile regression. Motivated by well-documented stylized facts, including heavy tails, volatility clustering, and regime-dependent variance, the analysis examines volatility regimes and quantile-specific return behavior in a parsimonious and interpretable setting. First, the Markov-Switching model identifies distinct low- and high-volatility regimes, with high transition persistence (volatility regimes, with high transition persistence (volatility regimes, with high transition persistence (volatility regimes, with high transition persistence (volatility regimes, with high transition persistence (volatility regimes, with high transition persistence (volatility regimes, with high transition persistence (volatility regimes, with high transition persistence (p00=0.9914, p11=0.9861) and expected durations of approximately 116 and 72 trading days, respectively. Second, quantile regression estimates at τ=0.05, τ=0.50, and τ=0.95 indicate that lagged returns have limited explanatory power in the lower and upper tails, while median returns exhibit weak mean reversion. These findings underscore the limitations of linear constant-variance models and highlight the episodic nature of risk in foreign exchange markets. Rather than proposing a new estimator, the paper contributes by offering a transparent two-stage empirical perspective that links regime identification with tail-risk analysis and can inform regime-aware risk monitoring in highly liquid highly liquid highly liquid highly liquid highly liquid highly liquid highly liquid highly liquid FX markets.highly liquid FX markets.

Keywords

EUR/USD
Markov-Switching
Quantile Regression
Volatility Clustering
Tail Risk
[1] D. Ardia, K. Boudt, and L. Catania, Generalized autoregressive conditional heteroskedasticity models with Markov-switching: The R package MSGARCH, Journal of Statistical Software, (2018) 85, 1–28.
[2] T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, (1986) 31, 307–327.
[3] T. Bollerslev, R. Y. Chou, and K. F. Kroner, ARCH modeling in finance: A review of the theory and empirical evidence, Journal of Econometrics, (1992) 52, 5–59.
[4] R. Cont, Empirical properties of asset returns: Stylized facts and statistical issues, Quantitative Finance, (2001) 1, 223–236.
[5] C. Engel, and J. D. Hamilton, Long swings in the dollar: Are they in the data and do markets know it?, American Economic Review, (1990) 80, 689–713.
[6] R. F. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, (1982) 50, 987–1007.
[7] E. F. Fama, The behavior of stock-market prices, Journal of Business, (1965) 38, 34–105.
[8] J. Geweke, and G. Amisano, Hierarchical Markov mixture models for cryptocurrency and exchange rate volatility, Journal of Applied Econometrics, (2011) 26, 608–633.
[9] S. F. Gray, Modeling the conditional distribution of interest rates as a regime-switching process, Journal of Financial Economics, (1996) 42, 27–62.
[10] M. Haas, S. Mittnik, and M. S. Paolella, A new class of Markov-switching GARCH models, Journal of Financial Econometrics, (2004) 2, 493–530.
[11] J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, (1989) 57, 357–384.
[12] C.-J. Kim, and C. R. Nelson, State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications, MIT Press, (1999).
[13] R. Koenker, and G. Bassett, Regression quantiles, Econometrica, (1978) 46, 33–50.
[14] R. Koenker, and Z. Xiao, Quantile autoregression, Journal of the American Statistical Association, (2006) 101, 980–990.
[15] T. Lee, I. C. Moutzouris, N. C. Papapostolou, and M. Fatouh, Foreign exchange hedging using regime-switching models: The case of pound sterling, International Journal of Finance & Economics, (2023) 28:4, 3985–4004.
[16] Y. Liu, Quantile regression with Markov switching, Journal of Econometrics, (2013) 173, 50–67.
[17] M. Lubrano, and A. A. Ndoye, Bayesian forecasting of Value-at-Risk using regime-switching models, International Journal of Forecasting, (2021) 37, 650–672.
[18] B. Mandelbrot, The variation of certain speculative prices, Journal of Business, (1963) 36, 394–419.
[19] K. M. Murphy, and R. H. Topel, Estimation and inference in two-step econometric models, Journal of Business & Economic Statistics, (2002) 20, 88–97.
[20] D. B. Nelson, Conditional heteroskedasticity in asset returns: A new approach, Econometrica, (1991) 59, 347–370.
[21] A. Pagan, Econometric issues in the analysis of regressions with generated regressors, International Economic Review, (1984) 25, 221–247.
[22] M. Tao, and L. Yin, Markov-switching quantile regression with time-varying transition probabilities, Journal of Applied Econometrics, (2022) 37, 453–472.
[23] S. J. Taylor, Modelling Financial Time Series, John Wiley & Sons, 1986.
 
Journal of Mathematics and Modeling in Finance

Articles in Press, Accepted Manuscript
Available Online from 21 August 2026

  • Receive Date 21 February 2026
  • Revise Date 28 July 2026
  • Accept Date 17 August 2026

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