Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

Bollerslev, Tim; Sizova, Natalia; Tauchen, George

doi:10.2139/ssrn.1687985

Cited by 33 publications

(41 citation statements)

References 59 publications

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“…But our results nicely complement those of Zhou (2009) andBollerslev, Sizova and. Using high-frequency intraday returns on the 6 In this study, bad and good news are determined by negative and positive innovations in returns and volatility.…”

Section: Introductionsupporting

confidence: 70%

“…They also observe it is consistent with the predictions of a long-run volatility risk equilibrium model. Bollerslev, Sizova and Tauchen (2009) rely on an equilibrium continuous-time model to capture this fact as well as the asymmetry in the relationship between volatility and past and future returns (leverage and volatility feedback effects).…”

Section: Introductionmentioning

confidence: 99%

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Measuring High-Frequency Causality Between Returns, Realized Volatility, and Implied Volatility

Dufour

García

Taamouti

2011

Journal of Financial Econometrics

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Section: Introductionsupporting

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Measuring High-Frequency Causality Between Returns, Realized Volatility, and Implied Volatility

Dufour

García

Taamouti

2011

Journal of Financial Econometrics

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“…literature; see, e.g., Bollerslev et al (2012) and the many additional references therein. 14 The q (0) t term is formally given by 1 2 σ 2 t + R (e x − 1 − x) ν t (dx).…”

Section: Continuous and Discontinuous Market Risk Pricingmentioning

confidence: 99%

Roughing Up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns

Bollerslev

Todorov³

2014

SSRN Journal

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Motivated by the implications from a stylized equilibrium pricing framework, we investigate empirically how individual equity prices respond to continuous, or "smooth," and jumpy, or "rough," market price moves, and how these different market price risks, or betas, are priced in the cross-section of expected returns. Based on a novel highfrequency dataset of almost one-thousand individual stocks over two decades, we find that the two rough betas associated with intraday discontinuous and overnight returns entail significant risk premiums, while the intraday continuous beta is not priced in the cross-section. An investment strategy that goes long stocks with high jump betas and short stocks with low jump betas produces significant average excess returns. These higher risk premiums for the discontinuous and overnight market betas remain significant after controlling for a long list of other firm characteristics and explanatory variables previously associated with the cross-section of expected stock returns.JEL classification: C13, C14, G11, G12 (2004), the habit persistence model of Campbell and Cochrane (1999), and the rare disaster model of Gabaix (2012), as special cases obtained by further restricting the functional form of the pricing kernel and the set of other priced risk factors. 1The statistical theory underlying our estimation of the separate betas builds on recent advances in financial econometrics related to the use of high-frequency intraday data and so-called realized volatilities. Bollerslev and Zhang (2003), Barndorff-Nielsen and Shephard (2004a), and Andersen et al. (2005, 2006, in particular, have previously explored the use of high-frequency data and the asymptotic notion of increasingly finer sampled returns over fixed time intervals for more accurately estimating realized betas. In contrast to these earlier studies, which do not differentiate among different types of market price moves, we rely on the theory originally developed by Todorov and Bollerslev (2010) for explicitly estimating separate continuous and discontinuous betas for the open-to-close active part of the trading day, together with overnight betas for the close-to-open returns. 5Our actual empirical investigations are based on a novel high-frequency dataset of all the 985 stocks included in the S&P 500 index over the 1993-2010 sample period. We begin by estimating the three separate betas as well as a standard CAPM regression-based beta for each of the individual stocks on a rolling one-year basis. Consistent with the basic tenets of the simple CAPM, we find that sorting the stocks in our sample on the basis of their betas, results in a positive return differential between the High-and Low-beta quantile portfolios for all of the four different beta estimates. 6 However, even though all of the return differentials are quite large numerically, the difference in the monthly returns between the High-and Low-beta portfolios constructed on the basis of the standard CAPM betas is not significantly different from zero at conventional lev...

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“…It is measured as the difference between (the square of) the CBOE VIX index and the statistical expectation of the future return variation. In Bollerslev et al (2009), Drechsler and Yaron (2010) and Bollerslev, Sizova, and Tauchen (2012), the return predictability of the

V R P

is investigated using a self‐contained general equilibrium model. This is in the spirit of the long‐run risks (LRR) model pioneered by Bansal and Yaron (2004).…”

Section: Introductionmentioning

confidence: 99%

“…This is in the spirit of the long‐run risks (LRR) model pioneered by Bansal and Yaron (2004). Specifically, Bollerslev et al (2009) and Bollerslev et al (2012) extend the LRR model by allowing the time‐varying volatility‐of‐volatility (vol‐of‐vol) within the economy to be generated by its own stochastic process. They further show that the difference between the risk‐neutral and the objective expectations of return variation isolates the vol‐of‐vol factor, which then serves as the sole source of the true

V R P

.…”

Section: Introductionmentioning

confidence: 99%

Return predictability of variance differences: A fractionally cointegrated approach

Izzeldin

Yao

2020

Journal of Futures Markets

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This paper examines the fractional cointegration between downside (upside) components of realized and implied variances. A positive association is found between the strength of their cofractional relation and the return predictability of their differences. That association is established via the common longmemory component of the variances that are fractionally cointegrated, which represents the volatility-of-volatility factor that determines the variance premium. Our results indicate that market fears play a critical role not only in driving the long-run equilibrium relationship between implied-realized variances but also in understanding the return predictability. A simulation study further verifies these claims. K E Y W O R D S fractional cointegration, return predictability, variance risk premium J E L C L A S S I F I C A T I O N C14; C32; C51 | INTRODUCTIONNumerous empirical studies suggest that, unlike the variance, the variance risk premium (VRP) carries nontrivial predictive power for aggregate stock market returns over quarterly to annual horizons, where the degree of return predictability is greater than that afforded by more conventional predictors, see, Bollerslev, Tauchen, and Zhou (2009), Drechsler and Yaron (2010), Bollerslev, Marrone, Xu, and Zhou (2014), and Bali and Zhou (2016), among others. Those studies also provide strong evidence that much of the predictability implicit in the VRP may be attributed to its close relation with macroeconomic uncertainty and aggregate risk aversion.The VRP is formally defined as the wedge between option-implied and realized variances. It is measured as the difference between (the square of) the CBOE VIX index and the statistical expectation of the future return variation. In Bollerslev et al. (2009), Drechsler andYaron (2010) and Bollerslev, Sizova, and Tauchen (2012), the return predictability of the VRP is investigated using a self-contained general equilibrium model. This is in the spirit of the long-run risks (LRR) model pioneered by Bansal and Yaron (2004). Specifically, Bollerslev et al. (2009) andBollerslev et al. (2012) extend the LRR model by allowing the time-varying volatility-of-volatility (vol-of-vol) within the economy to be generated by its own stochastic process. They further show that the difference between the risk-neutral and the objective expectations of return variation isolates the vol-of-vol factor, which then serves as the sole source of the true VRP. The VRP, therefore, displays good predictive power for future returns in cases where the vol-of-vol plays a more dominant role in determining variation in the equity premium. A direct link between the VRP and the vol-of-vol is also demonstrated in a purely probabilistic model introduced by Barndorff-Nielsen and Veraart (2013). U D . The SJ and IVA are, respectively, measured as the difference between RV U and RV D and the difference between IV U and IV D . Using a semiparametric approach, we demonstrate the existence of a fractionally cointegrating relation in each pair of the semivariances...

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Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

Cited by 33 publications

References 59 publications

Measuring High-Frequency Causality Between Returns, Realized Volatility, and Implied Volatility

Measuring High-Frequency Causality Between Returns, Realized Volatility, and Implied Volatility

Roughing Up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns

Return predictability of variance differences: A fractionally cointegrated approach

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