Elsevier

Journal of Financial Markets

Volume 42, January 2019, Pages 29-55
Journal of Financial Markets

Intraday information from S&P 500 Index futures options

https://doi.org/10.1016/j.finmar.2018.10.001Get rights and content

Highlights

  • Use of intraday high frequency transaction price data of E-mini index futures and index futures options.

  • Extract risk-neutral volatility, skewness, and kurtosis.

  • Perform forecasting of next interval moments using various models.

  • Employ forecast risk-neutral moments to form options trading strategies.

  • Find profitable skewness trading strategy.

Abstract

In this paper, we employ the intraday transaction prices of liquid E-mini S&P 500 index futures options to form 10-min ahead risk-neutral skewness forecasts and show profitable options trading strategy net of transaction costs. We do not find profitable trading based on 10-min ahead risk-neutral volatility and only very marginal cases of profitable trading using kurtosis forecasts. The skewness profitability anomaly may be an indication of informational inefficiency in intraday S&P 500 futures options trading, which is contrary to findings using longer-span daily and weekly moments. Our results lend credence to the persistence of intraday trading activities in the markets.

Introduction

We study the intraday dynamics of risk-neutral moments of S&P 500 Index futures prices, and test intraday informational market efficiency in the index futures options market. There have been many tests of daily, weekly, and monthly options prices and the general deduction of market efficiency. However, there are relatively few studies on the efficiency of intraday information derived from the traded prices of index or index futures options. In this paper, we employ information of risk-neutral moments on S&P 500 Index futures returns extracted from liquid E-mini Index futures options to form 10-min ahead forecasts and develop profitable option trading strategies. We find that strategies capturing risk-neutral skewness information are profitable net of transaction costs. We do not find profitable trading based on 10-min ahead risk-neutral volatility and only very marginal cases of profitable trading using kurtosis forecasts.

Neumann and Skiadopoulos (2013) use daily S&P 500 Index options over January 1996 to October 2010 to extract risk-neutral moments for forecasting and for testing trading strategies over one-day, one-week, and one-month horizons. They find that all the risk-neutral moments can generally be predicted better out-of-sample relative to the random walk benchmark. Using one-day ahead forecasts of the risk-neutral moments to pre-determine option trades, they find that except for the one-day ahead skewness forecast, the other moment forecasts did not support profitable trading. After considering transaction cost in the form of the bid-ask spread, they report that skewness forecasts also did not deliver positive profitability. The results were similar for forecasts involving longer horizons of a week or longer. They thus conclude that the hypothesis of the efficiency of the S&P 500 Index options market cannot be rejected.

Earlier studies had also investigated if a one-day ahead volatility forecast can lead to profitable option trading net of transaction costs. Using S&P 500 Index options and forecasts based on the history of implied volatility from the Black-Scholes model, Gonçalves and Guidolin (2006) find positive profit using OLS regression for forecast and applying a $0.25 round-trip transaction cost (see their Table 8), but this is reduced to a loss when a higher round-trip transaction cost of $0.50 is applied. Similarly Harvey and Whaley (1992) identify implied volatility from short-term, nearest at-the-money S&P 100 options, and conclude that one-day ahead forecasts of volatility are accurate, but such forecasts did not provide for profitable option trading after transaction cost was accounted for. However, Noh et al. (1994) find that a GARCH forecast of volatility using S&P 500 Index returns applied to straddle trading produced significant profit of up to 0.89% average daily return based on a $0.50 filter and a round-trip transaction cost of $0.25. They also find that a forecast using implied volatilities did not produce profitable results.

The cited studies basically find historical prices to be useful in predicting the future volatility of the stock indices, and they then check for profitability via options trading based on the forecast volatility. Profitability net of transaction cost would indicate market inefficiency with respect to the historical price information. Non-profitability would support the maintained hypothesis of market efficiency. Predictability on volatility is possible with both market efficiency and market inefficiency. Neumann and Skiadopoulos (2013) open up a new line of enquiry into efficiency on the options market by testing daily trading strategies based also on risk-neutral skewness and risk-neutral kurtosis forecasts. The risk-neutral probability distribution of the underlying asset to an option embodies a large amount of information on market expectations, as well as its risk preferences. In a 2013 NYU Stern–Federal Reserve Conference on Risk Neutral Probability Density, Figlewski (2013) suggested that searching for profitable trading strategies is a good question for research. This is indeed a clever insight as trading profitability not only has obvious attractions for the finance industry, but it also has deep implications on theory.

Risk-neutral probability information via risk-neutral volatility, skewness, and kurtosis are forward-looking with a particular maturity associated with the options from which the moments are extracted. Most studies in recent years use the extraction method by Bakshi et al. (2003) that is known to be model-free. The idea behind forecasting and trading is to try to beat the market by taking a long or short position in the portfolio of options after the forecast is made and before the market forms the value of the portfolio next period. The risk-neutral moments also serve as ex-ante proxy measures of the underlying return volatility, skewness, and kurtosis. Other areas of studies such as in equilibrium asset pricing make use of these ex-ante measures to explain cross-sectional stock returns.

Chang et al. (2013) estimate risk-neutral moments from daily S&P 500 Index option data. They find that risk-neutral market-wide or aggregate skewness is an important risk factor in explaining the cross-section of stock returns, and yields a robustly negative risk premium. Bali and Murray (2013) use monthly stock options data from 1996 to 2010 to extract individual stock risk-neutral skewness with a one-month forward horizon. They form monthly portfolios of skewness assets sorted based on deciles of the extracted skewness, and find a strong negative relation between the skewness of asset returns and risk-neutral skewness, indicating investor preference for idiosyncratic risk-neutral skewness. Conrad et al. (2013) use daily individual option prices from 1996 to 2005 to infer their underlying stock return risk-neutral moments over horizons from one-month to one-year. They find that the individual stock's moments were strongly related to future returns after controlling for other firm characteristics, and provide evidence of risk premiums in idiosyncratic moments.

Clearly empirical results in asset pricing have indicated highly relevant forward-looking and dynamic information contained in the risk-neutral moments of stocks or of an aggregated index from traded options. In equilibrium, assuming market investors hold optimal portfolios aligned with their risk preferences, they also receive the risk premiums for undertaking positions with risks, such as for example, receiving on average over time a higher return for portfolios with higher volatility, negative skewness, and larger kurtosis. Such forward-looking and dynamic information in the risk-neutral moments or the conditional moments naturally provide history of the moments as fodder for forecasting what the next period risk-neutral distribution and therefore what the prices of the portfolio of options may be. As prices change dynamically throughout each trading day, there should be a huge interest to explore the dynamics or conditional moments within a trading day. These intraday trading forecasts and forecast-based intraday trading receives time-averaged profits, if any, due to informational superiority over the market, but the informational advantages would not correlate with market factors and thus are not compensation for risk premium.

Our paper makes a number of contributions to the literature in the area of intraday futures options trading profitability and intraday equity futures index return moments predictability. As far as we know, our study is one of the first on intraday implied moments of S&P 500 Index futures returns using intraday or high-frequency futures option prices. Firstly, we use intraday E-mini S&P 500 European-style futures options data and improve on existing techniques to extract the first four moments of the risk-neutral return distribution. Secondly, we perform intraday out-of-sample forecasting or prediction, and also document the intraday dynamics of the index futures return risk-neutral moments. We also introduce a novel local autoregression method that allows variable window in fitting the autoregressive parameters. This is particularly useful in situations when there may be intraday news that cause structural changes in the returns or price distributions. It also distinguishes itself from the conventional autoregressive model with predetermined sample lengths. Thirdly, we show profitability in the trading strategies involving the various risk-neutral moment forecasts, particularly those involving skewness. The positive profitability after transaction costs in skewness trading indicates an anomaly that may be an indication of market inefficiency in intraday options trading – it could be due to information inefficiency within short spans of time as in 10-min intervals. We also explain why persistence is not necessarily the only condition for accurate out-of-sample forecasts and the resulting profitability.

In Section 2, we discuss the method for extracting the risk-neutral moments. The data and implementation procedures are then explained. Section 3 provides a discussion of the forecasting models used in the forecast of intraday 10-min ahead risk-neutral moments. The local autoregressive model is also explained. Section 4 contains the empirical results showing the forecasting performances of the various models. Section 5 provides the results based on different option trading strategies involving the risk-neutral moment forecasts. A sub-section provides a discussion of the persistence of the risk-neutral moments and the relationship with our forecasting and trading performances. We report results trying to forecast intraday 10-min ahead futures returns based on information of ex-ante risk-neutral moments in Section 6. Section 7 contains our conclusions.

Section snippets

Implied risk-neutral moments

Predictions of returns moments for the purposes of financial trading, hedging, and asset pricing, is prevalent in finance. The most common forecast is that of predictive means usually obtained from a regression model. More general frameworks for setting up predictability ranges from the modeling of stochastic models to time series modeling such as GARCH. For forecasting realized volatility, Andersen et al. (2003) is a fundamental paper on the modeling and forecasting of high-frequency intraday

Forecasting models

In this section, we describe the regression models that we use to fit the time series of each of the risk-neutral moments. For each of the three different risk-neutral moments, the regressions are also performed on different time series belonging to the different constant maturities. For ease of exposition, we use the notation RNMt(τ) to represent any of the three risk-neutral moments at time t, or the tth interval, with maturity τ. More specifically RNVt(τ), RNSt(τ), and RNKt(τ) denote

Forecasting performance

After the regression models are estimated, the estimated coefficients are used to provide a fitted model for the purpose of predicting the next period or future RNMs. Parameters are estimated in the window on the same day from 8:40 a.m. to 12:00 p.m., after which the fitted model is used for forecasting during 12:10 p.m. to 2:50 p.m. Unlike daily or weekly methods, we do not use rolling windows over the 10-min intervals within a trading day. This helps in focusing on days with highly liquid

Options trading strategies

Using the forecasts generated by the seven competing models of AR lag-one, ARMA(1,1), AR(1) with GARCH error, VAR lag-one, VAR(1) with GARCH errors, VECM, and LAR, we attempt to construct a trading strategy to benefit from the accurate forecast of the various future moment changes. RW is excluded as it has served its purpose for benchmark comparison in the forecast assessments shown in Table 3, Table 4, Table 5, Table 6. Besides, our seven competing models outperform RW in terms of MCP. We now

Ex-ante moments and subsequent returns

In single period asset pricing or intertemporal asset pricing with stationary stochastic investment opportunities, there is a majority of models where higher systematic covariance, systematic co-kurtosis, and lower co-skewness are compensated by higher expected returns. Theoretical papers include Kraus and Litzenberger (1976) and Harvey and Siddique (2000) on co-skewness, and Dittmar (2002) on co-kurtosis. In a somewhat similar setup, across portfolios of stocks that are left-skewed, have high

Conclusions

As far as we know, ours is one of the first studies on the intraday implied moments of S&P 500 Index futures returns using intraday or high-frequency futures option prices and the E-mini Index futures prices. The E-mini S&P 500 Index futures options are European-style and the data are actual transactions prices on the CME Exchange. First, we improve on existing techniques by using cubic hermite interpolation with better smoothing properties to extract the first four moments of the risk-neutral

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    We acknowledge helpful comments on earlier versions of the paper from faculty participants at the Singapore Management University Symposium, the National University of Singapore RMI Seminar, the International Institute of Forecaster's Korean Conference, the Statistical Computing Asia Conference at Taipei Academia Sinica, and the Australasian Finance and Banking Conference. The insightful comments of the referee were particularly important. We are also grateful for the programming assistance of Chua Wee Song. Funding from the OUB Chair is gratefully acknowledged.

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