Abstract: This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of cross-sectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: 1) an increase in trading volume relative to trend over the prior six months; and 2) positive returns over the prior thirty-six months. The first finding is consistent with the model of Hong and Stein (1999), which predicts that negative asymmetries are more likely to occur when there are large differences of opinion among investors. The latter finding fits with a number of theories, most notably Blanchard and Watson’s (1982) rendition of stockprice bubbles. Analogous results also obtain when we attempt to forecast the skewness of the aggregate stock market, though our statistical power in this case is limited.

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 paper explains the presence and evolution of risk-neutral skewness over time and in the cross-section of individual stocks.

An implicit method is developed for the numerical solution of option pricing models where it is assumed that the underlying process is a jump diffusion. This method can be applied to a variety of contingent claim valuations, including American options, various kinds of exotic options, and models with uncertain volatility or transaction costs. Proofs of timestepping stability and convergence of a fixed point iteration scheme are presented. For typical model parameters, it is shown that the fixed point iteration reduces the error by two orders of magnitude at each iteration. The correlation integral is computed using a fast Fourier transform (FFT) method. Techniques are developed for avoiding wrap-around effects. Numerical tests of convergence for a variety of options are presented.

. Statistical analysis of data from the nancial markets shows that generalized hyperbolic (GH) distributions allow a more realistic description of asset returns than the classical normal distribution. GH distributions contain as subclasses hyperbolic as well as normal inverse Gaussian (NIG) distributions which have recently been proposed as basic ingredients to model price processes. GH distributions generate in a canonical way Levy processes, i.e. processes with stationary and independent increments. We introduce a model for price processes which is driven by generalized hyperbolic Levy motions. This GH model is a generalization of the hyperbolic model developed by Eberlein and Keller (1995). It is incomplete. We derive an option pricing formula for GH driven models using the Esscher transform as martingale measure and compare the prices with classical Black-Scholes prices. The objective of this study is to examine the consistency of our model assumptions with the empirically obser...

We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to volatility risk, derivatives enable non-myopic investors to exploit the time-varying opportunity set; and as a means of exposure to jump risk, they enable investors to disentangle the simultaneous exposure to diffusive and jump risks in the stock market. Calibrating to the S&P 500 index and options markets, we find sizable portfolio improvement from derivatives investing.

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We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of at-the-money and out-of-the-money options as the option maturity approaches zero. We show that these prices converge to zero at speeds which depend upon whether the sample path of the underlying asset price process is purely continuous, purely discontinuous, or a mixture of both. By applying the test to S&P 500 index options data, we conclude that the sample path behavior of this index contains both a continuous component and a jump component. In particular, we find that while the presence of the jump component varies strongly over time, the presence of the continuous component is constantly felt. We investigate the implications of the evidence for parametric model specifications.

A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from high-frequency returns coupled with relatively simple reduced form time series modeling procedures. Building on recent theoretical results from Barndorff-Nielsen and Shephard (2003c) for related bi-power variation measures involving the sum of high-frequency absolute returns, the present paper provides a practical framework for non-parametrically measuring the jump component in the realized volatility measurements. Exploiting these ideas for a decade of high-frequency five-minute returns for the DM/ $ exchange rate, the S&P500 aggregate market index, and the 30-year U.S. Treasury Bond, we find the jump components to be distinctly less persistent than the contribution to the overall return variability originating from the continuous sample path component of the price process. Explicitly including the jump measure as an additional explanatory variable in an easy-to-implement reduced form model for the realized volatilities results in highly significant jump coefficient estimates at the daily, weekly and quarterly forecasts horizons. As such, our results hold promise for improved financial asset allocation, risk management, and derivatives pricing, by separate modeling, forecasting and pricing of the continuous and jump components of the total return variability.

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a shortdated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.

We analyze the specifications of option pricing models based on time-changed Lévy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the S&P 500 index options, we must incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component.