Is volatility risk priced in the securities market? Evidence from S&P 500 index options

The authors examine whether volatility risk is a priced risk factor in securities returns. Zero‐beta at‐the‐money straddle returns of the S&P 500 index are used to measure volatility risk. It is demonstrated that volatility risk captures time variation in the stochastic discount factor. The results suggest that straddle returns are important conditioning variables in asset pricing, and investors use straddle returns when forming their expectations about securities returns. One interesting finding is that different classes of firms react differently to volatility risk. For example, small firms and value firms have negative and significant volatility coefficients, whereas big firms and growth firms have positive and significant volatility coefficients during high‐volatility periods, indicating that investors see these latter firms as hedges against volatile states of the economy. Overall, these findings have important implications for portfolio formation, risk management, and hedging strategies. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:617–642, 2007     

The information content of the S&P 500 index and VIX options on the dynamics of the S&P 500 index

Given that both S&P 500 index and VIX options essentially contain information about the future dynamics of the S&P 500 index, in this study, we set out to empirically investigate the informational roles played by these two option markets with regard to the prediction of returns, volatility, and density in the S&P 500 index. Our results reveal that the information content implied from these two option markets is not identical. In addition to the information extracted from the S&P 500 index options, all of the predictions for the S&P 500 index are significantly improved by the information recovered from the VIX options. Our findings are robust to various measures of realized volatility and methods of density evaluation. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Has the introduction of S&P 500 ETF options led to improvements in price discovery of SPDRs?

This study sets out to investigate trading in Standard and Poor's Depository Receipt Trust Series I (SPDR) options and the impact on the price‐discovery process of SPDRs. The empirical results reveal a significant rise in liquidity within the SPDR market following the introduction of SPDR options. Furthermore, the results also show that the introduction of SPDR options has led to a significant improvement in the information share of SPDRs, and that the contribution of SPDRs to price discovery has become very close to that of E‐mini index futures. These findings imply that developments in the derivatives market can lead to improvements in market quality, including the level of liquidity and price discovery of the underlying securities. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:683–711, 2012     

Testing mean reversion in financial market volatility: Evidence from S&P 500 index futures

This article presents a comprehensive study of continuous time GARCH (generalized autoregressive conditional heteroskedastic) modeling with the thintailed normal and the fat‐tailed Student's‐t and generalized error distributions (GED). The study measures the degree of mean reversion in financial market volatility based on the relationship between discrete‐time GARCH and continuoustime diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean‐reverting behavior of futures market volatility. The empirical evidence obtained from the S&P 500 index futures indicates that the conditional variance, log‐variance, and standard deviation of futures returns are pulled back to some long‐run average level over time. The study also compares the performance of alternative GARCH models with normal, Student's‐ t, and GED density in terms of their power to predict one‐day‐ahead realized volatility of index futures returns and provides some implications for pricing futures options. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1–33, 2008     

Pricing efficiency of the S&P 500 index market: Evidence from the Standard & Poor's Depositary Receipts

Standard & Poor's Depositary Receipts (SPDRs) are exchange traded securities representing a portfolio of S&P 500 stocks. They allow investors to track the spot portfolio and better engage in index arbitrage. We tested the impact of the introduction of SPDRs on the efficiency of the S&P 500 index market. Ex‐post pricing efficiency and ex‐ante arbitrage profit between SPDRs and futures were also examined. We found an improved efficiency in the S&P 500 index market after the start of SPDRs trading. Specifically, the frequency and length of lower boundary violations have declined since SPDRs began trading. This result is consistent with the hypothesis that SPDRs facilitate short arbitrage by simplifying the process of shorting the cash index against futures. Tests of pricing efficiency comparing SPDRs and futures suggested that index arbitrage using SPDRs as a substitute for program trading in general results in losses. Although short arbitrages earn a small profit on average, gains are statistically insignificant. A trade‐by‐trade investigation showed that prices are instantaneously corrected after the presence of mispricing signals, introducing substantial risk in arbitraging. Evidence in general supported pricing efficiency between SPDRs and the S&P 500 index futures—both ex‐post and ex‐ante. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:877–900, 2002     

Standard and Poor’s depository receipts and the performance of the S&P 500 index futures market

In response to the need for a simple financial instrument that enables retail investors to participate easily and quickly in the U.S. equity market and that facilitates basket trading by institutions, the American Stock Exchange introduced Standard and Poor’s Depository Receipts (SPDRs) on January 29, 1993. The purpose of this study is to determine the effects of the introduction of SPDRs on the pricing efficiency of the S&P futures market. Using a measure of efficiency that is based on the difference between the observed futures price and the theoretical futures price based on the Cost of Carry Model, as well as daily and intradaily data for the period January 2, 1990 through June 3, 1996, we found that some positive mispricing was reduced when SPDR’s were introduced. While dividend yield and time‐to‐maturity biases remained, SPDRs trading was shown to mitigate the extent of pricing errors that prevailed, and reduced the effects of dividend yield and time‐to‐maturity biases found for these contracts. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:705–716, 2000     

Clustering in the futures market: Evidence from S&P 500 futures contracts

We document trade price clustering in the futures markets. We find clustering at prices of x.00 and x.50 for S&P 500 futures contracts. While trade price clustering is evident throughout time to maturity of these contracts, there is a dramatic change when the S&P 500 futures contract is designated a front‐month contract (decrease in clustering) and a back‐month contract (increase in clustering). We find that trade price clustering is a positive function of volatility and a negative function of volume or open interest. In addition, we find a high degree of clustering in the daily opening and closing prices, but a lower degree of clustering in the settlement prices. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:413–428, 2004     

Pricing and hedging S&P 500 index options with Hermite polynomial approximation: empirical tests of Madan and Milne's model

The universal use of the Black and Scholes option pricing model to value a wide range of option contracts partly accounts for the almost systematic use of Gaussian distributions in finance. Empirical studies, however, suggest that there is an information content beyond the second moment of the distribution that must be taken into consideration.This article applies a Hermite polynomial-based model developed by Madan and Milne (1994) to an investigation of S&P 500 index option prices from the CBOE when the distribution of the underlying index is unknown. The model enables us to incorporate the non-normal skewness and kurtosis effects empirically observed in option-implied distributions of index returns. Out-of-sample tests confirm that the model outperforms Black and Scholes in terms of pricing and hedging. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 735–758, 1999     

A Multivariate Stochastic Volatility Model Applied to a Panel of S&P500 Stocks in Different Industries

We estimate a multivariate stochastic volatility model for a panel of stock returns for a number of S&P 500 firms from different industries. To directly compare our results with those from the univariate estimation literature on the same data, we use an efficient importance sampling (EIS) method to estimate the likelihood function of the given multivariate system that we analyze. As opposed to univariate methods where each return is estimated separately for each firm, our results are based on joint estimation that can account for potential common error term interactions based on industry characteristics that cannot be detected by univariate methods. Our results reveal that there are important differences in the industry effects, something that suggests that differential gains to portfolio allocations in the different industries that we examine. There are differences because of idiosyncratic factors and the common industry factors that suggest that each industry requires a separate treatment in arriving at portfolio allocations.