AI 中文总结
本研究用GARCH、GJR-GARCH及两区制马尔可夫转换GARCH模型分析美元远期互换利率波动率，发现MSGARCH能稳定区制参数并捕捉时变特征，虽BIC偏好简约模型，但其结构解释更清晰。
AI 中文摘要
我们使用GARCH(1,1)、GJR-GARCH(1,1)和两区制马尔可夫转换GARCH（MSGARCH）模型，研究了美元1年期远期互换利率（USD 1Yx10Y forward swap rate）的条件波动率动态。该分析使用了2007年至2023年的日度数据，并结合了市场隐含指标（ATM swaption波动率和SRVIX指数）以及一系列广泛的诊断测试。标准GARCH和GJR-GARCH模型显示出稳定的短期参数，但截距项{\omega}在不同滚动窗口间变化显著，导致隐含的长期方差不稳定。这一模式经Nyblom检验确认，促使我们采用区制转换设定。MSGARCH通过保持区制特定参数的稳定性，并利用滤波后的区制概率捕捉时变特征，缓解了这一问题。它提供了最高的对数似然值和最低的AIC，而BIC则更倾向于更简约的GJR-GARCH模型。一步向前回测表明，各模型在短期预测精度上相当，但MSGARCH通过分离与主要市场事件一致的高波动率和低波动率区制，提供了更清晰的结构性解释。
英文摘要
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.
