The VIX as Stochastic Volatility for Corporate Bonds

ArXiv ID: 2410.22498 “View on arXiv”

Authors: Unknown

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.

Keywords: stochastic volatility models, VIX, autoregression, corporate bonds, residual analysis, Fixed Income (Corporate Bonds)

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical models, including autoregressive stochastic volatility frameworks with non-standard assumptions (e.g., observable VIX, dependent innovations), requiring significant mathematical formulation and theoretical proofs of stationarity and ergodicity. Empirically, it is backtest-ready with specific data sources (FRED), multiple bond market segments, code availability on GitHub, and detailed metrics like skewness and kurtosis for model validation.

  flowchart TD
    A["Research Goal<br>Use VIX as observable volatility<br>to model corporate bonds"] --> B["Data Input<br>Moody's AAA/BAA &<br>Bank of America IG/HY"]
    A --> C["Data Input<br>S&P 500 VIX"]
    B --> D["Methodology<br>Autoregression on Rates & Spreads<br>vs Treasury"]
    C --> E["Methodology<br>Normalize Residuals<br>Divide by VIX"]
    D --> F["Computational Process<br>Analyze Residuals<br>Verify Gaussian White Noise"]
    E --> F
    F --> G["Key Findings<br>Long-term model stability<br>VIX effective for corporate bonds"]