Modeling interest rate swap volatility with GARCH processes

Micha{\l} Balcerek and Micha{\l} Wronka

Papers from arXiv.org

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 {\omega} 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.

Date: 2026-09
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