The VIX as Stochastic Volatility for Corporate Bonds

TL;DR

This paper introduces a novel approach to modeling corporate bond volatility by using the VIX index as a stochastic volatility proxy, improving residual Gaussianity and model fit across different bond segments.

Contribution

It applies the VIX to observe and incorporate stochastic volatility in corporate bond models, enhancing residual properties and model stability compared to traditional methods.

Findings

Residuals become closer to Gaussian white noise after division by VIX.

Models show long-term stability across different bond segments.

VIX-based stochastic volatility improves model fit for corporate bonds.

Abstract

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.