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 offers a tractable monetary asset pricing model. In monetary economies, the price level, inflation, asset prices, and the real and nominal interest rates have to be determined simultaneously and in relation to each other. This link allows us to relate in closed form each of the dependent entities to the underlying real and monetary variables. Among other features of such economies, inflation can be partially nonmonetary and the real and nominal term structures can depend on fundamentally different risk factors. In one extreme, the process followed by the real term structure is independent of that followed by its nominal counterpart.]

In existing theory, wealth is no more valuable than its implied consumption rewards. In reality investors acquire wealth not just for its implied consumption, but for the resulting social status. Max M. Weber refers to this desire for wealth as the spirit of capitalism. We examine, both analytically and empirically, implications of Weber's hypothesis for consumption, savings, and stock prices. When investors care about relative social status, propensity to consume and risk-taking behavior will depend on social standards, and stock prices will be volatile. The spirit of capitalism seems to be a driving force behind stock-market volatility and economic growth.

This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the risk-neutral density. Third, we derive laws that decompose individual return skewness into a systematic component and an idiosyncratic component. Empirical analysis of OEX options and 30 stocks demonstrates that individual risk-neutral distributions differ from that of the market index by being far less negatively skewed. This article explains the presence and evolution of risk-neutral skewness over time and in the cross section of individual stocks.

This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the risk-neutral density. Third, we derive laws that decompose individual return skewness into a systematic component and an idiosyncratic component. Empirical analysis of OEX options and 30 stocks demonstrates that individual risk-neutral distributions differ from that of the market index by being far less negatively skewed. This article explains the presence and evolution of risk-neutral skewness over time and in the cross section of individual stocks.

This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using S&P 500 options, we find that sampled intraday (or interday) call (put) prices often go down (up) even as the underlying price goes up, and call and put prices often increase, or decrease, together. Our results are valid after controlling for time decay and market microstructure effects. Therefore one-dimensional diffusion option models cannot be completely consistent with observed option price dynamics; options are not redundant securities, nor ideal hedging instruments-puts and the underlying asset prices may go down together.

This article studies the equilibrium valuation of foreign exchange contingent claims. Within a continuous-time Lucas (1982) two-country model, exchange rates, interest rates, and, in particular, factor risk prices are all endogenously and jointly determined. This guarantees the internal consistency of these price processes with a general equilibrium. In the same model, closed-form valuation formulas are presented for currency options and currency futures options. Common to these formulas is that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statics are also provided analytically. It is shown that most existing currency option models are included as special cases.

How reliable is the recovery theorem of Ross (2015)? We explore this question in the context of options on the 30-year Treasury bond futures, allowing us to deduce restrictions that link the physical and risk-neutral return distributions. Our empirical results undermine the implications of the recovery theorem. First, we reject an implicit assumption of the recovery theorem that the martingale component of the stochastic discount factor is identical to unity. Second, we consider the restrictions between the physical and risk-neutral return moments when the recovery theorem holds, and reject them in both forecasting regressions and generalized method of moments estimations.

Substantial progress has been made in developing more realistic option pricing models. Empirically, however, it is not known whether and by how much each generalization improves option pricing and hedging. The authors fill this gap by first deriving an option model that allows volatility, interest rates, and jumps to be stochastic. Using S&P 500 options, they examine several alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant time-series data, (2) out-of-sample pricing, and (3) hedging. Overall, incorporating stochastic volatility and jumps is important for pricing and internal consistency. But for hedging, modeling stochastic volatility alone yields the best performance.

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.