Classic stochastic volatility models assume volatility is unobservable. We use the Volatility Index: S\&P 500 VIX to observe it, to easier fit the model. We apply it to corporate bonds. We fit autoregression for corporate rates and for risk spreads between these rates and Treasury rates. Next, we divide residuals by VIX. Our main idea is such division makes residuals closer to the ideal case of a Gaussian white noise. This is remarkable, since these residuals and VIX come from separate market segments. Similarly, we model corporate bond returns as a linear function of rates and rate changes. Our article has two main parts: Moody's AAA and BAA spreads; Bank of America investment-grade and high-yield rates, spreads, and returns. We analyze long-term stability of these models.

翻译：经典随机波动率模型假定波动率不可观测。我们采用波动率指数：标准普尔500 VIX对其进行观测，以简化模型拟合过程。我们将该方法应用于公司债券领域。首先对公司债券利率及其与国债利率间的风险利差进行自回归拟合。随后，将残差项除以VIX值。我们的核心观点是：该除法运算能使残差更接近理想的高斯白噪声状态——这一现象尤为显著，因为残差与VIX源自不同的市场板块。类似地，我们将公司债券收益率建模为利率及其变化的线性函数。本文主要包含两部分实证研究：穆迪AAA级与BAA级债券利差；美国银行投资级与高收益债券的利率、利差及收益率。最后，我们分析了这些模型的长期稳定性特征。