Crashes, Volatility, and the Equity Premium: Lessons from S&amp;P 500 Options

Santa-Clara, Pedro; Yan, Shu

doi:10.1162/rest.2010.11549

Cited by 309 publications

(89 citation statements)

References 56 publications

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“…The mean realized excess return of the DAX is 0.0189, which is much lower than the 6.6% stated by Mehra and Prescott (2003) for the period 1978-1997, and the median is 0.1217. Taking the median as a proxy for the total equity risk premium, more than 50% of the total risk premium can be attributed to compensation for rare events, which is similar to the values found by Santa-Clara and Yan (2010). The annual realized risk premium and the model equity risk premium due to rare events series are depicted in Figure 5.…”

Section: Figure 4: Equity and Variance Risk Premia For The German Stosupporting

confidence: 65%

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Investor Fears and Risk Premia for Rare Events

Schwarz

2014

SSRN Journal

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Reproduction permitted only if source is stated.ISBN 978-3-95729-010-6 (Printversion) Non-technical summary A risk premium is the compensation demanded by investors for holding a financial asset with risky payoffs that exceeds the risk-free rate. A recent strand of literature believes that the fear of large negative shocks is a component that drives asset prices because investors expect compensation for the risk that such a rare event occurs. This paper aims at estimating equity risk premia that are due to the compensation for rare events. Rare events, such as the collapse of Lehman in September 2008, trigger large price jumps and are seldomly observed in the data which makes it hard to estimate the distribution of such events. I use a newly developed method to extract price jumps from option data and high frequency futures price data of the S&P 500 for estimating the distribution of rare events and the equity risk premia for the US stock market. In addition, the method allows for constructing an investor fear index. I replicate the method expanding the data sample to include more recent years. Furthermore, I apply the method to German data using the DAX as the proxy for the German stock market.The compensation for rare events accounts for a considerable part of the equity risk premia in both stock markets. The results are much higher than the results of similar analyses. The investor fear index works very well, as it spikes at all significant events that moved the stock markets. But the correlation of the fear index with commonly used volatility indices such as the VIX for the US market and the VDAX for the German market is about 90%. Moreover, in the financial crisis the fear index spikes only after the Lehman default, whereas indicators based on credit spreads increase sharply much earlier. Therefore, the fear index appears to be inappropriate as an early-warning tool but describes the prevalent situation in the stock markets well. Bollerslev and Todorov (2011b) to estimate risk premia for extreme events for the US and the German stock markets. The method extracts jump tail measures from high-frequency futures price data and from options data. In a second step, jump tail distributions are approximated using the extreme value theory. Applying the method to German data yields very similar results to the ones shown for the US data. The risk premia for rare events constitute a considerable part of the total equity and variance risk premia for both markets. When using the results to build an investor fear index for the US and Germany, I find that the correlation of the fear index for the US with the VIX is 89.5% and that of the fear index for Germany with the VDAX is 90.6%. Nicht-technische Zusammenfassung

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Section: Figure 4: Equity and Variance Risk Premia For The German Stosupporting

confidence: 65%

“…Pan (2002), Broadie, Chernov, and Johannes (2007), Todorov (2010) and Santa-Clara and Yan (2010). Broadie, Chernov, and Johannes (2009) analyze S&P 500 option portfolio returns and find that jump risk premia can explain parts of the returns.…”

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confidence: 99%

Investor Fears and Risk Premia for Rare Events

Schwarz

2014

SSRN Journal

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“…Several studies more squarely rooted in the options pricing literature have also explored the equilibrium implications of allowing for richer volatility dynamics and nonstandard preference structures; see, e.g., the recent papers by Benzoni et al (2005), Eraker andShaliastovich (2008) and Santa-Clara and Yan (2009) and the references therein. However, the empirical focus of the present paper is distinctly different from all of these other studies, and to the best of our knowledge, no other coherent economic equilibrium-based explanation for the volatility asymmetries and dynamic dependencies depicted in Figures 1 and 2 is yet available in the literature.…”

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confidence: 99%

Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

2009

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Stock market volatility clusters in time, carries a risk premium, is fractionally integrated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast in continuous-time and entirely self-contained, involving non-separable recursive preferences. We show that the qualitative theoretical implications from the new model match remarkably well with the distinct shapes and patterns in the sample autocorrelations of the volatility and the volatility risk premium, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes.

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“…Earlier structural works which address issues in option markets typically introduce jumps into the fundamental consumption process: see Eraker and Shaliastovich (2008), Drechsler and Yaron (2008), Santa-Clara and Yan (2008), Gabaix (2007), Bates (2006), Benzoni, Collin-Dufresne, and Goldstein (2005), Liu, Pan, and Wang (2005). In this paper, I do not entertain the possibility of jumps in consumption, and instead show that learning and fluctuating confidence about expected growth can account for the key features of option and equity data.…”

Section: Introductionmentioning

confidence: 77%

“…For GMM estimation, I consider moments of confidence measure and equity returns, which characterize non-Gaussian features of the distribution, as well as the information in interest rates and option-implied volatilities in the data. I also employ the latent-factor MLE approach, where I treat confidence measure as well as consumption volatility and expected growth state as latent factors and back them out from the option, return and consumption data, similar to Duffie and Singleton (1997), Pan (2002) and Santa-Clara and Yan (2008). The quantitative implications from the two estimation approaches are very similar and provide empirical support for the long-run risks model with learning, fluctuating investor confidence and jump-like confidence risks.…”

Section: Introductionmentioning

confidence: 97%

Learning, confidence, and option prices

Shaliastovich

2015

Journal of Econometrics

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Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options

Cited by 309 publications

References 56 publications

Investor Fears and Risk Premia for Rare Events

Investor Fears and Risk Premia for Rare Events

Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

Learning, confidence, and option prices

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