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Discussion Paper
Equity Volatility Term Premia
Investors can buy volatility hedges on the stock market using variance swaps or VIX futures. One motivation for hedging volatility is its negative relationship with the stock market. When volatility increases, stock returns tend to decline contemporaneously, a result known as the leverage effect. In this post, we measure the cost of volatility hedging by decomposing the prices of variance swaps and VIX futures into volatility forecasts and estimates of expected returns (“equity volatility term premia”) from January 1996 to June 2020.
Working Paper
Bank Interventions and Options-based Systemic Risk: Evidence from the Global and Euro-area Crisis
Using a novel dataset on central bank interventions to financial institutions, we examine the impact of capital injection announcements on systemic risk for the banking sector in the U.S. and the euro area between 2008 and 2013. We propose a new measure of options-based systemic risk called downside correlation risk premium (DCRP), which quantifies the compensation investors demand for being exposed to the risk of large correlated drops in bank stock prices. DCRP is calculated using options that provide a hedge against large drops in the price of a bank index and its individual components. We ...
Working Paper
Taxonomy of Global Risk, Uncertainty, and Volatility Measures
A large number of measures for monitoring risk and uncertainty surrounding macroeconomic and financial outcomes have been proposed in the literature, and these measures are frequently used by market participants, policy makers, and researchers in their analyses. However, risk and uncertainty measures differ across multiple dimensions, including the method of calculation, the underlying outcome (that is, the asset price or macroeconomic variable), and the horizon at which they are calculated. Therefore, in this paper, we review the literature on global risk, uncertainty, and volatility ...
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Equity Volatility Term Premia
This paper estimates the term-structure of volatility risk premia for the stock market. Realized variance term premia are increasing in systematic risk and predict variance swap returns. Implied volatility term premia are decreasing in risk initially, but then increase at a lag, predicting VIX futures returns. By modeling the logarithm of realized variance, the paper derives a closed-form relationship between the prices of variance swaps and VIX futures. The model provides accurate pricing and highlights periods of dislocation between the index options and VIX futures markets. Term premia ...
Discussion Paper
The Law of One Price in Equity Volatility Markets
Can option traders take a square root? Surprisingly, maybe not. This post shows that VIX futures prices exhibit significant deviations from their option-implied upper bounds—the square root of variance swap forward rates—thus violating the law of one price, a fundamental concept in economics and finance. The deviations widen during periods of market stress and predict the returns of VIX futures. Just as the stock market struggles with multiplication, the equity volatility market appears unable to take a square root at times.
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Global variance term premia and intermediary risk appetite
Sellers of variance swaps earn time-varying risk premia for their exposure to realized variance, the level of variance swap rates, and the slope of the variance swap curve. To measure risk premia, we estimate a dynamic term structure model that decomposes variance swap rates into expected variances and term premia. Empirically, we document a strong global factor structure in variance term premia across the U.S., U.K., Europe, and Japan. We further show that variance term premia are negatively correlated with the risk appetite of hedge funds, broker-dealers, and mutual funds. Our results ...
Working Paper
Term Structure of Interest Rates with Short-run and Long-run Risks
Bond returns are time-varying and predictable. What economic forces drive this variation? To answer this long-standing question, we propose a consumption-based model with recursive preferences, long-run risks, and inflation non-neutrality. Our model offers two important insights. First, our model matches well the post-1990 nominal upward-sloping U.S. Treasury yield curve. Second, consistent with our model's implication, variance risk premium based on the U.S. interest rate derivatives data emerges as a strong predictor for short-horizon Treasury excess returns, above and beyond the predictive ...
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Option-implied term structures
This paper proposes a nonparametric sieve regression framework for pricing the term structure of option spanning portfolios. The framework delivers closed-form, nonparametric option pricing and hedging formulas through basis function expansions that grow with the sample size. Novel confidence intervals quantify term structure estimation uncertainty. The framework is applied to estimating the term structure of variance risk premia and finds that a short-run component dominates market excess return predictability. This finding is inconsistent with existing asset pricing models that seek to ...
Working Paper
Variance Risk Premium Components and International Stock Return Predictability
In this paper, we document and explain the distinct behaviors of U.S. downside and upside variance risk premiums (DVP and UVP, respectively) and their international stock return predictability patterns. DVP, the compensation for bearing downside variance risk, is positive, highly correlated with the total variance premium, and countercyclical, whereas UVP is, on average, borderline positive and procyclical with large negative spikes around episodes of market turmoil. We then provide robust evidence that decomposing VP into its downside and upside components significantly improves domestic and ...
Working Paper
The Response of Stock Market Volatility to Futures-Based Measures of Monetary Policy Shocks
In this paper, we investigate the dynamic response of stock market volatility to changes in monetary policy. Using a vector autoregressive model, our findings reveal a significant and asymmetric response of stock returns and volatility to monetary policy shocks. Although the increase in the volatility risk premium, futures-trading volume, and leverage appear to contribute to a short-term increase in volatility, the longer-term dynamics of volatility are dominated by monetary policy's effect on fundamentals. The estimation results from a bivariate VAR-GARCH model suggest that the Fed does not ...