We investigate whether the volatility risk premium is negative by examining the statistical properties of delta-hedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium and the mean delta-hedged portfolio returns. Using a sample of S&P 500 index options, we provide empirical tests that have the following general results. First, the delta-hedged strategy underperforms zero. Second, the documented underperformance is less for options away from the money. Third, the underperformance is greater at times of higher volatility.Fourth, the volatility risk premium significantly affects delta-hedged gains even after accounting for jump-fears. Our evidence is supportive of a negative market volatility risk premium.

This article presents a framework for studying the role of recovery on defaultable debt prices for a wide class of processes describing recovery rates and default probability. These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be employed to infer the market expectation of recovery rates implicit in bond prices. Empirical implementation of these models suggests two central findings. First, the recovery concept that specifies recovery as a fraction of the discounted par value has broader empirical support. Second, parametric debt valuation models can provide a useful assessment of recovery rates embedded in bond prices.

We examine the effect of regularly scheduled macroeconomic announcements on the beliefs and preferences of participants in the U.S. Treasury market by comparing the option-implied state-price density (SPD) of bond prices shortly before and after the announcements. We find that the announcements reduce the uncertainty implicit in the second moment of the SPD regardless of the content of the news. The changes in the higher-order moments, in contrast, depend on whether the news is good or bad for economic prospects. Using a standard model for interest rates to disentangle changes in beliefs and changes in preferences, we demonstrate that our results are consistent with time-varying risk aversion in the spirit of habit formation. We thank Tim Bollerslev, Jun Cai, and Frank Song for providing the announcements data and Nick

Regulations allow market makers to short sell without borrowing stock, and the transactions of a major options market maker show that in most hard-to-borrow situations, it chooses not to borrow and instead fails to deliver stock to its buyers. Some of the value of failing passes through to option prices: when failing is cheaper than borrowing, the relation between borrowing costs and option prices is significantly weaker. The remaining value is profit to the market maker, and its ability to profit despite the usual competition between market makers appears to result from a cost advantage of larger market makers at failing.

This article investigates option models in the encompassing class of stochastic volatility, returnjumps, and volatility-jumps. Relying on individual equity options and method of simulated moments estimation, several major results obtained are, first, that the double-jump process is the least misspecified and the least demanding in fitting the tail-size and tail-asymmetry of individual risk-neutral return distributions; second, the double-jump model improves pricing performance beyond return-jumps absent volatility-jumps, and beyond volatility-jumps absent return-jumps; third, between return-jumps and volatility-jumps, the former is empirically more relevant than the latter for pricing options; fourth, the inverse link between volatility-jumps and return-jumps is instrumental for explaining the valuation of deep out-of-money puts and option dynamics of firms with high kurtosis; fifth, stochastic volatility is not as important for individual equity options as it is for index options. Incremental insights that emerge from individual equity options bring clarity to divergent findings on the role of return-jumps and volatility-jumps.

Preliminary and incomplete. Please do not quote or cite. We use a sample of option prices, and the method of Bakshi, Kapadia and Madan (2003), to estimate the ex ante higher moments of the underlying individual securities ’ risk-neutral returns distribution. We find that individual securities ’ volatility, skewness and kurtosis are strongly related to subsequent returns. Consistent with Ang, Hodrick, Xing and Zhang (2006), we find a negative relation between cross-sectional volatility and returns. We also find a significant relation between skewness and returns, with more negatively (positively) skewed returns associated with subsequent higher (lower) returns, while kurtosis is positively related to returns. We analyze the extent to which these returns relations represent compensation for risk. We use data on index options and the underlying market return to estimate the stochastic discount factor over the 1996-2005 sample period, and allow the stochastic discount factor to include higher moments. We find evidence that, even after controlling for differences in co-skewness, individual securities ’ skewness matters. All errors are the responsibility of the authors. We thank Robert Battalio, Patrick Dennis, and Stewart Mayhew for providing data and computational code. We thank seminar participants at Babson College,

We use a sample of option prices, and the method of Bakshi, Kapadia and Madan (2003), to estimate the ex ante higher moments of the underlying individual securities ’ risk-neutral returns distribution. We find that individual securities ’ volatility, skewness and kurtosis are strongly related to subsequent returns. Specifically, we find a negative relation between volatility and returns in the cross-section. We also find a significant relation between skewness and returns, with more negatively (positively) skewed returns associated with subsequent higher (lower) returns, while kurtosis is positively related to subsequent returns. To analyze the extent to which these returns relations represent compensation for risk, we use data on index options and the underlying index to estimate the stochastic discount factor over the 1996-2005 sample period, and allow the stochastic discount factor to include higher moments. We find evidence that, even after controlling for differences in co-moments, individual securities ’ skewness matters. However, when we combine information in the risk-neutral distribution and the stochastic discount factor to estimate the implied physical distribution of industry returns, we find little evidence that the distribution of technology stocks was positively skewed during the bubble period–in fact, these stocks have the lowest skew, and the highest estimated Sharpe ratio, of all stocks in our sample. All errors are the responsibility of the authors. We thank Robert Battalio, Patrick Dennis, and Stewart Mayhew for providing data and computational code. We thank Andrew Ang, Leonce Bargeron, and Paul Pfleiderer

This paper proposes a pricing model for the FDIC's reinsurance risk. We derive a closed-form Weibull call option pricing model to price a call-spread a reinsurer might sell to the FDIC. To obtain the risk-neutral loss-density necessary to price this call spread we risk-neutralize a Weibull distributed FDIC annual losses by a tilting coecient estimated from the traded call options on the BKX index. An application of the proposed approach yield reasonable reinsurance prices and also shows that tilting is embedded in the FDIC's risk-based insurance premiums.

The market's risk neutral probability distribution for the value of an asset on a future date can be extracted from the prices of a set of options that mature on that date, but two key technical problems arise. In order to obtain a full well-behaved density, the option market prices must be smoothed and interpolated, and some way must be found to complete the tails beyond the range spanned by the available options. This paper develops an approach that solves both problems, with a combination of smoothing techniques from the literature and a new method of completing the density with tails drawn from a Generalized Extreme Value distribution. We extract ten years of daily risk neutral densities from S&P 500 index options and find that they are quite different from the lognormal densities assumed in the Black-Scholes framework, and that their shapes change in a regular way as the underlying index moves. Our approach is quite general and has the potential to reveal valuable insights about how information and risk preferences are incorporated into prices in many financial markets.

Thanks to Justin Birru for excellent assistance on this research and to Otto van Hemert,