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This paper studies the positive and normative implication of extreme shocks for monetary policy. The analysis is based on a small-scale new Keynesian model with sticky prices and wages where shocks are drawn from asymmetric generalized extreme value (GEV) distributions. A nonlinear perturbation of the model is estimated by the simulated method of moments. Under both the Taylor and Ramsey policies, the central bank responds nonlinearly and asymmetrically to shocks. The trade-off between targeting a gross inaation rate above 1 as insurance against extreme shocks and strict price stability is unambiguously decided in favour of strict price stability.

Variance swaps are natural instruments for investors taking directional bets on volatility and are often used for portfolio protection. The empirical observation on skewness research suggests that derivative professionals may also desire to hedge beyond volatility risk and there exists the need to hedge higher-moment market risks, such as skewness and kurtosis risks. We study two derivative contracts – skewness swap and kurtosis swap – which trade the forward realized third and fourth cumulants. Using S&P 500 index options data from 1996 to 2005, we document the returns of these swap contracts, i.e., skewness risk premium and kurtosis risk premium. We find that the both skewness and kurtosis risk premiums are significantly negative.

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.

This paper investigates nonlinear pricing kernels in which the risk factor is endogenously determined and preferences restrict the definition of the pricing kernel. These kernels potentially generate the empirical performance of nonlinear and multifactor models, while maintaining empirical power and avoiding ad hoc specifications of factors or functional form. Our test results indicate that preferencerestricted nonlinear pricing kernels are both admissible for the cross section of returns and are able to significantly improve upon linear single- and multifactor kernels. Further, the nonlinearities in the pricing kernel drive out the importance of the factors in the linear multi-factor model.

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.

This article develops a new method for inferring risk-neutral probabilities (or state-contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and, hence, consistent with all the observed option prices). A simple backwards recursive procedure solves for the entire tree. From the standpoint of the standard binomial option pricing model, which implies a limiting risk-neutral lognormal distribution for the underlying asset, the approach here provides the natural (and probably the simplest) way to generalize to arbitrary ending risk-neutral probability distributions. Copyright 1994 by American Finance Association.