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Report
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.
Working Paper
Ambiguity, Long-Run Risks, and Asset Prices
I generalize the long-run risks (LRR) model of Bansal and Yaron (2004) by incorporatingrecursive smooth ambiguity aversion preferences from Klibanoff et al. (2005, 2009) and time-varyingambiguity. Relative to the Bansal-Yaron model, the generalized LRR model is as tractable but moreflexible due to its separation of ambiguity aversion from both risk aversion and the intertemporalelasticity of substitution. This three-way separation allows the model to further account for thevariance premium puzzle besides the puzzles of the equity premium, the risk-free rate, and the returnpredictability. ...
Working Paper
Learning, Rare Disasters, and Asset Prices
In this paper, we examine how learning about disaster risk affects asset pricing in an endowment economy. We extend the literature on rare disasters by allowing for two sources of uncertainty: (1) the lack of historical data results in unknown parameters for the disaster process, and (2) the disaster takes time to unfold and is not directly observable. The model generates time variation in the risk premium through Bayesian updating of agents' beliefs regarding the likelihood and severity of disaster realization. The model accounts for the level and volatility of U.S. equity returns and ...
Report
The Law of One Price in Equity Volatility Markets
This paper documents law of one price violations in equity volatility markets. While tightly linked by no-arbitrage restrictions, the prices of VIX futures exhibit significant deviations relative to their option-implied upper bounds. Static arbitrage opportunities occur when the prices of VIX futures violate their bounds. The deviations widen during periods of market stress and predict the returns of VIX futures. A relative value trading strategy based on the deviation measure earns a large Sharpe ratio and economically significant alpha-to-margin. There is evidence that systematic risk and ...
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
Examining the Sources of Excess Return Predictability: Stochastic Volatility or Market Inefficiency?
We use a consumption based asset pricing model to show that the predictability of excess returns on risky assets can arise from only two sources: (1) stochastic volatility of fundamental variables, or (2) departures from rational expectations that give rise to predictable investor forecast errors and market inefficiency. While controlling for stochastic volatility, we find that a variable which measures non-fundamental noise in the Treasury yield curve helps to predict 1-month-ahead excess stock returns, but only during sample periods that include the Great Recession. For these sample ...
Report
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 ...
Report
The Global Credit Cycle
Do global credit conditions affect local credit and business cycles? Using a large cross-section of equity and corporate bond market returns around the world, we construct a novel global credit factor and a global risk factor that jointly price the international equity and bond cross-section. We uncover a global credit cycle in risky asset returns, which is distinct from the global risk cycle. We document that the global credit cycle in asset returns translates into a global credit cycle in credit quantities, with a tightening in global credit conditions predicting extreme capital flow ...