The Term Structure of the Price of Variance Risk

AbstractThis paper performs specification analysis on the term structure of variance swap rates on the S&P 500 index and studies the optimal investment decision on the variance swaps and the stock index. The analysis identifies 2 stochastic variance risk factors, which govern the short and long end of the variance swap term structure variation, respectively. The highly negative estimate for the market price of variance risk makes it optimal for an investor to take short positions in a short-term variance swap contract, long positions in a long-term variance swap contract, and short positions in the stock index.

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Risk Premia and the VIX Term Structure

Journal of Financial and Quantitative Analysis ◽

10.1017/s0022109017000825 ◽

2017 ◽

Vol 52 (6) ◽

pp. 2461-2490 ◽

Cited By ~ 26

Author(s):

Travis L. Johnson

Keyword(s):

Term Structure ◽

Principal Component ◽

Risk Premia ◽

Expectations Hypothesis ◽

Variance Swaps ◽

Volatility Index ◽

Asset Pricing Models ◽

Vix Futures ◽

Synthetic Standard ◽

Variance Risk

The shape of the Chicago Board Options Exchange Volatility Index (VIX) term structure conveys information about the price of variance risk rather than expected changes in the VIX, a rejection of the expectations hypothesis. The second principal component, SLOPE, summarizes nearly all this information, predicting the excess returns of synthetic Standard & Poor’s (S&P) 500 variance swaps, VIX futures, and S&P 500 straddles for all maturities and to the exclusion of the rest of the term structure. SLOPE’s predictability is incremental to other proxies for the conditional variance risk premia, economically significant, and inconsistent with standard asset pricing models.

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The Price of the Smile and Variance Risk Premia

Management Science ◽

10.1287/mnsc.2020.3689 ◽

2020 ◽

Author(s):

Peter H. Gruber ◽

Claudio Tebaldi ◽

Fabio Trojani

Keyword(s):

Term Structure ◽

Risk Premium ◽

Implied Volatility ◽

Risk Premia ◽

State Variables ◽

State Spaces ◽

State Process ◽

Joint Dynamics ◽

Variance Risk ◽

Implied Volatility Surfaces

Using a new specification of multifactor volatility, we estimate the hidden risk factors spanning S&P 500 index (SPX) implied volatility surfaces and the risk premia of volatility-sensitive payoffs. SPX implied volatility surfaces are well-explained by three dependent state variables reflecting (i) short- and long-term implied volatility risks and (ii) short-term implied skewness risk. The more persistent volatility factor and the skewness factor support a downward sloping term structure of variance risk premia in normal times, whereas the most transient volatility factor accounts for an upward sloping term structure in periods of distress. Our volatility specification based on a matrix state process is instrumental to obtaining a tractable and flexible model for the joint dynamics of returns and volatilities, which improves pricing performance and risk premium modeling with respect to recent three-factor specifications based on standard state spaces. This paper was accepted by Gustavo Manso, finance.

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Inflation Risk Premia, Yield Volatility, and Macro Factors

Journal of Financial Econometrics ◽

10.1093/jjfinec/nby004 ◽

2018 ◽

Vol 17 (3) ◽

pp. 397-431 ◽

Cited By ~ 1

Author(s):

Andrea Berardi ◽

Alberto Plazzi

Keyword(s):

Term Structure ◽

Risk Premium ◽

Implied Volatility ◽

Risk Premia ◽

Output Growth ◽

Inflation Risk ◽

Variance Risk Premium ◽

Real Risk ◽

Variance Risk ◽

Inflation Risk Premia

Abstract We incorporate a latent stochastic volatility factor and macroeconomic expectations in an affine model for the term structure of nominal and real rates. We estimate the model over 1999–2016 on U.S. data for nominal and TIPS yields, the realized and implied volatility of T-bonds, and survey forecasts of GDP growth and inflation. We find relatively stable inflation risk premia averaging at 40 basis points at the long-end, and which are strongly related to the volatility factor and conditional mean of output growth. We also document real risk premia that turn negative in the post-crisis period, and a non-negligible variance risk premium.

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The Variance Swaps based on KOSPI200 Index and the Term Structure of Variance Risk Premium

Journal of Derivatives and Quantitative Studies ◽

10.1108/jdqs-04-2013-b0004 ◽

2013 ◽

Vol 21 (4) ◽

pp. 435-463

Author(s):

Young Ho Eom ◽

Woon Wook Jang

Keyword(s):

Risk Factors ◽

Term Structure ◽

Risk Premium ◽

Risk Averse ◽

Realized Variance ◽

Over The Counter ◽

Variance Swaps ◽

Variance Swap ◽

Variance Risk Premium ◽

Variance Risk

This study examines whether the variance risk is a priced risk factor in Korea using the over-the-counter variance swap quotes and realized variance data. We also study the term structure of variance risk premium. The empirical results show that the model with 2 stochastic variance risk factors with jumps in return is required to fit the variance swap and realized variance data. The analyses with the estimated models suggest that the variance risk premium in Korea are highly negative and the size of the premium increase with the maturities, meaning that risk averse investors in Korea are willing to pay a premium to hedge variance risk.

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