The jump component of S&P 500 volatility and the VIX index

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.     

SV mixture models with application to S&P 500 index returns

Understanding both the dynamics of volatility and the shape of the distribution of returns conditional on the volatility state is important for many financial applications. A simple single-factor stochastic volatility model appears to be sufficient to capture most of the dynamics. It is the shape of the conditional distribution that is the problem. This paper examines the idea of modeling this distribution as a discrete mixture of normals. The flexibility of this class of distributions provides a transparent look into the tails of the returns distribution. Model diagnostics suggest that the model, SV-mix, does a good job of capturing the salient features of the data. In a direct comparison against several affine-jump models, SV-mix is strongly preferred by Akaike and Schwarz information criteria.     

Returns and option activity over the option-expiration week for S&P 100 stocks

For S&P 100 stocks, we find that the weekly returns over option-expiration (OE) weeks (a month’s third-Friday week) tend to be high, relative to: (1) the third-Friday weekly returns of other stocks with less option activity, (2) the own stock’s other weekly returns, (3) the risk, based on asset-pricing alphas. For these same stocks, a month’s fourth-Friday weekly returns underperform modestly. We suggest the following two avenues are likely partial contributors towards understanding these return patterns: (1) delta-hedge rebalancing by option market makers, with a reduction in short-stock hedge positions over the OE week, and (2) declining risk perceptions over the OE week, as measured by option-derived implied volatilities. Our findings suggest option activity can induce reliable patterns in the weekly returns of option-active large-cap stocks.     

Hedging the black swan: Conditional heteroskedasticity and tail dependence in S&P500 and VIX

The recent financial crisis has accentuated the fact that extreme outcomes have been overlooked and not dealt with adequately. While extreme value theories have existed for a long time, the multivariate variant is difficult to handle in the financial markets due to the prevalent heteroskedasticity embedded in most financial time series, and the complex extremal dependence that cannot be conveniently captured by a single structure. Moreover, most of the existing approaches are based on a limiting argument in which all variables become large at the same rate. In this paper, we show how the conditional approach of Heffernan and Tawn (2004) can be implemented to model extremal dependence between financial time series. We use a hedging example based on VIX futures to demonstrate the flexibility and superiority of the conditional approach against the conventional OLS regression approach.     

A comprehensive long-term analysis of S&P 500 index additions and deletions

We investigate the long-term effects of S&P 500 index additions and deletions on a sample of stocks from 1962 to 2003 and find a significant long-term price increase for both added and deleted stocks, with deleted stocks outperforming added stocks. The long-term price increase for added stocks can be attributed to increases in institutional ownership, liquidity, and analyst coverage, and a decrease in the shadow cost in the long-term. However, while deletion has no significant effect on analyst coverage and shadow cost, we find a rebound in the institutional ownership and liquidity of deleted stocks. The difference in the long-term price increase of added and deleted stocks can be explained by analyst coverage and operating performance.     

Pinning in the S&P 500 futures

We show that Standard & Poor's (S&P) 500 futures are pulled toward the at-the-money strike price on days when serial options on the S&P 500 futures expire (pinning) and are pushed away from the cost-of-carry adjusted at-the-money strike price right before the expiration of options on the S&P 500 index (anti-cross-pinning). These effects are driven by the interplay of market makers' rebalancing of delta hedges due to the time decay of those hedges as well as in response to reselling (and early exercise) of in-the-money options by individual investors. The associated shift in notional futures value is at least $115 million per expiration day.     

Volatility dynamics for the S&P 500: Further evidence from non-affine,multi-factor jump diffusions

We apply Markov chain Monte Carlo methods to time series data on S&P 500 index returns, and to its option prices via a term structure of VIX indices, to estimate 18 different affine and non-affine stochastic volatility models with one or two variance factors, and where jumps are allowed in both the price and the instantaneous volatility. The in-sample fit to the VIX term structure shows that the second (stochastic long-term volatility) factor is required to fit the VIX term structure. Out-of-sample tests on the fit to individual option prices, as well as in-sample tests, show that the inclusion of jumps is less important than allowing for non-affine dynamics. The estimation and testing periods together cover more than 21 years of daily data.     

Cross-section of option returns and volatility

We study the cross-section of stock option returns by sorting stocks on the difference between historical realized volatility and at-the-money implied volatility. We find that a zero-cost trading strategy that is long (short) in the portfolio with a large positive (negative) difference between these two volatility measures produces an economically and statistically significant average monthly return. The results are robust to different market conditions, to stock risks-characteristics, to various industry groupings, to option liquidity characteristics, and are not explained by usual risk factor models.     

The S&P500 index effect reconsidered: Evidence from overnight and intraday stock price performance and volume

This study focuses on S&P500 inclusions and deletions, examining the impact of potential overnight price adjustment after the announcement of an S&P500 index change. We find evidence of a significant overnight price change that diminishes the returns available to speculators although there are still profits available from the first day after announcement until a few days after the actual event. More importantly, observing the tick-by-tick stock price performance and volume effects on the key days during the event window for the first time, we find evidence of consistent trading patterns during trading hours. A separate analysis of NASDAQ and NYSE listed stocks allows for a detailed examination of the price and volume effect at an intra-day level. We find that index funds appear to cluster their rebalancing activities near to and after the close on the event date, suggesting that they are more concerned with tracking error than profit.     

Strategic trading by index funds and liquidity provision around S&P 500 index additions

We examine the trades of index funds and other institutions around S&P 500 index additions. We find index funds begin rebalancing their portfolios with the announcement of composition changes and do not fully establish their positions until weeks after the effective date. Trading away from the effective date is more prevalent for stocks with lower levels of liquidity and among large index funds, which is consistent with index funds accepting higher tracking error in order to reduce the price impact of their trades. Small and mid-cap funds provide liquidity to index funds around additions, and added stocks with a greater proportion of these natural liquidity providers experience lower inclusion returns.     

FORECASTING STOCK INDEX VOLATILITY: COMPARING IMPLIED VOLATILITY AND THE INTRADAY HIGH–LOW PRICE RANGE

The intraday high–low price range offers volatility forecasts similarly efficient to high‐quality implied volatility indexes published by the Chicago Board Options Exchange (CBOE) for four stock market indexes: S&P 500, S&P 100, NASDAQ 100, and Dow Jones Industrials. Examination of in‐sample and out‐of‐sample volatility forecasts reveals that neither implied volatility nor intraday high–low range volatility consistently outperforms the other.     

Determinants of S&;P 500 index option returns

We analyze common factors that affect returns on S&P 500 index options and find that 93% of the variation in option returns can be explained by three factors, which respectively account for 87%, 4%, and 2% of the variation in option returns. Furthermore, we test diffusion option pricing models by using mean–variance spanning properties implied in the models. The spanning tests reject one-factor diffusion models, as well as the hypothesis that the underlying asset and an equally weighted option index span options. Our results fail to reject that the underlying asset and an at-the-money option can span out-of-the-money options, but does reject that they span in-the-money options.      

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

Predicting stock returns: A regime-switching combination approach and economic links

This paper introduces a regime-switching combination approach to predict excess stock returns. The approach explicitly incorporates model uncertainty, regime uncertainty, and parameter uncertainty. The empirical findings reveal that the regime-switching combination forecasts of excess returns deliver consistent out-of-sample forecasting gains relative to the historical average and the Rapach et al. (2010) combination forecasts. The findings also reveal that two regimes are related to the business cycle. Based on the business cycle explanation of regimes, excess returns are found to be more predictable during economic contractions than during expansions. Finally, return forecasts are related to the real economy, thus providing insights on the economic sources of return predictability.     

An advanced perspective on the predictability in hedge fund returns

This paper advances the research on the predictability in hedge fund returns, using a broad set of risk factors within a variety of different prediction models. Accounting for the fact that returns are non-normally distributed, heteroscedastic and time-varying in their exposure to pervasive economic risk factors, we advocate a non-parametric backward elimination regression approach. The interdependencies between the monthly changes of envisaged risk factors and the subsequent hedge fund returns remain remarkably stable in terms of the observed direction of impact. Thus, taking into account the specific characteristics of this asset class, we find strong evidence of its return predictability.     

On the predictability of stock prices: A case for high and low prices

This paper contributes to technical analysis (TA) literature by showing that the high and low prices of equity shares are largely predictable only on the basis of their past realizations. Moreover, using their forecasts as entry/exit signals can improve common TA trading strategies applied on US equity prices. We propose modeling high and low prices using a simple implementation of a fractional vector autoregressive model with error correction (FVECM). This model captures two fundamental patterns of high and low prices: their cointegrating relationship and the long-memory of their difference (i.e., the range), which is a measure of volatility.     

Point and Figure charting: A computational methodology and trading rule performance in the S&P 500 futures market

This paper empirically contributes to the existing trading rule literature by providing a methodology for the calculation of Point and Figure charts using ultra-high-frequency data and tests trading rules using eight objective, pre-defined trading rules on S&P 500 futures contracts traded between 1990 and 1998. To assess the robustness of reported profits, a bootstrapping adjustment was conducted to determine the forecasting power of the PF trading rules. The results producing mixed statistical significance with some rules proving significant while many others were not.     

Changes in cash holdings around the S&P 500 additions

We analyze the changes in cash holding policies of S&P 500 firms from before to after their inclusion in the index. One year after inclusion, their mean industry-adjusted cash holdings decline by nearly 32% from the year before inclusion. Several factors explain this decline. The precautionary motive for cash subsides due to these firms becoming more visible, less uncertain, and less constrained to raise cheap external capital. Corporate governance deteriorates after inclusion due to increased managerial entrenchment, which leads to a reduction in cash as suggested by the free cash flow hypothesis. Most index firms face diminishing investment opportunities and decreasing capital expenditures, which implies a lesser need for cash holdings related to the transaction motive.     

The Samuelson hypothesis in futures markets: An analysis using intraday data

This paper considers the Samuelson hypothesis, which argues that the futures price volatility increases as the futures contract approaches its expiration. Utilizing intraday data from 20 futures markets in six futures exchanges, we find strong support for the Samuelson hypothesis in agricultural futures. However, the Samuelson hypothesis does not hold for other futures contracts. We also provide supporting evidence that the ‘negative covariance’ hypothesis is the key factor for the empirical support of the Samuelson hypothesis. In addition, our findings remain largely unaltered even after we control for seasonality and liquidity effects.     

Stock market momentum, business conditions, and GARCH option pricing models

This paper examines the forecasting performance of GARCH option pricing models from a market momentum perspective, and the possible impacts of financial crises and business conditions are also examined. The empirical results demonstrate that market momentum impacts the forecasting performance of GARCH option pricing models. The EGARCH model performs better under downward market momentum, while the standard GARCH performs better under upward market momentum. In addition, parsimonious models generally outperform richly parameterized ones. The above findings are robust to financial crises, and the results further demonstrate that business conditions influence the forecasting performance of GARCH option pricing models.