Paper: arXiv 2609.25965

Authors: Michał Balcerek, Michał Wronka

Abstract

We examine the conditional volatility dynamics of the USD 1Yx10Y forward swap rate using GARCH(1,1), GJR-GARCH(1,1), and a two-regime Markov-switching GARCH (MSGARCH) model. The analysis uses daily data from 2007 to 2023 and incorporates market-implied measures (ATM swaption volatility and the SRVIX in- dex) together with a broad set of diagnostic tests. Standard GARCH and GJR- GARCH models show stable short-run parameters, but the intercept ω varies markedly across rolling windows, causing instability in the implied long-run vari- ance. This pattern, confirmed by the Nyblom test, motivates adopting a regime- switching specification. MSGARCH mitigates this issue by keeping regime-specific parameters stable and capturing time variation through filtered regime probabili- ties. It delivers the highest log-likelihood and lowest AIC, whereas BIC favours the more parsimonious GJR-GARCH. One-step-ahead backtesting indicates comparable short-horizon accuracy across models, but MSGARCH offers a clearer structural in- terpretation by isolating high- and low-volatility regimes aligned with major market events.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper demonstrates a strong blend of advanced mathematical modeling (GARCH family, MSGARCH) with rigorous empirical validation using real-world financial data and comprehensive diagnostic tests. The application to interest rate swap volatility, including comparisons with market-implied measures, showcases a robust quantitative finance study.

Research Flowchart

  flowchart TD
    A[Research Goal: Model USD 1Yx10Y Forward Swap Rate Volatility] --> B{Key Methodology: GARCH, GJR-GARCH, MSGARCH};
    B --> C[Data/Inputs: Daily 2007-2023 1Yx10Y Fwd Swap Rate, ATM Swaption Vol, SRVIX];
    C --> D{Computational Processes: Model Estimation, Diagnostic Tests, Backtesting};
    D --> E[Key Findings/Outcomes: GARCH/GJR-GARCH ω instability, MSGARCH stable parameters, highest Log-Likelihood/lowest AIC, clear structural interpretation via regimes];