A multi-horizon comparison of density forecasts for the S&amp;P 500 using index returns and option prices

Shackleton, Mark B.; Taylor, Stephen J.; Yu, Peng

doi:10.1016/j.jbankfin.2010.05.006

Cited by 53 publications

(54 citation statements)

References 82 publications

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“…Consistent with the prior studies, including Bliss and Panigirtzoglou [2004], Anagnou-Basioudis et al [2005], Shackleton et al [2006], and Liu et al [2007], the RWDs provide satisfactory forecasts for the densities of future index levels for all prediction horizons, and indeed, these are not dependent on either the model specifications or the approaches used for the construction of the RWDs. All of the Anderson-Darling statistics are insignificant at a very high level, with the highest being those for the RWDs constructed under the SVJJ model.…”

Section: Density Predictionsupporting

confidence: 83%

“…The density transformation using this function was previously performed by Shackleton et al [2006] and Liu et al [2007]. The CDF of the beta distribution is defined as: (14) where B(α, β ) is the Beta function.…”

Section: Risk-neutral and Real-world Densitiesmentioning

confidence: 99%

“…As suggested by Shackleton et al [2006], we can also use an alternative non-parametric approach, that is, an empirical calibration function, to implement the transformation. Let φ(·) and Φ(·) denote, respectively, the PDF and CDF of the standard normal distribution.…”

Section: Risk-neutral and Real-world Densitiesmentioning

confidence: 99%

“…By contrast, regardless of whether we used the beta distribution or non-parametric calibration method, or whether or not jumps were incorporated, the RWDs provided consistently satisfactory density predictions for future FTSE 100 index levels. Shackleton et al [2006] derive the necessary and sufficient condition for the beta distribution calibrated density to imply a risk-averse utility function, α Յ 1 Յ β (with α β ). If either α > 1 or β < 1, then the representative agent is a risk-seeker for an interval of wealth, with respect to which the second derivative of the utility function is positive.…”

Section: Density Predictionmentioning

confidence: 99%

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The Impact of Jump Dynamics on the Predictive Power of Option-Implied Densities

Wang¹

2009

JOD

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This article examines whether incorporating jumps with stochastic volatility can improve the predictive power of option-implied densities of the FTSE 100 index. A general double-jump model is used to fit the market prices of options and to estimate "riskneutral" densities. "Real-world" densities are then converted from their risk-neutral form by means of alternative statistical calibrations. Both the risk-neutral and real-world densities are evaluated over five forecast horizons using two different tests. The empirical results indicate that adding jumps into the price and/or volatility processes not only substantially lowers the fitting errors of option prices, but also improves the predictive power of risk-neutral densities. Furthermore, satisfactory density prediction was consistently provided by the real-world densities, which were not dependent on the addition of jumps, the approach used to construct the densities, or the prediction horizon. Notes: Both the average and total numbers of settlement prices are provided for call options on the FTSE 100 index across "time-to-maturity" and "moneyness" for the years 2000-2005. All prices of put options are converted to their equivalent call prices using put-call parity; only out-of-the-money options are selected. Moneyness is defined by the ratio of the strike price to the forward price. Time-to-maturity is defined by the number of calendar days between trading and expiry dates. Figures in parentheses refer to the total number of option prices within each of the classifications. The average index levels across moneyness are also provided in the last column. Notes: The Anderson-Darling statistics are used to evaluate the predictive power of the RNDs and the RWDs estimated with alternative models from the FTSE 100 option prices for the years 2000-2005. The forecast horizons include 1 day, 1 week, 2 weeks, 3 weeks, and 4 weeks, with the periods for all horizons being non-overlapping. The RWDs are transformed from the RNDs using either parametric (beta distribution function) or non-parametric statistical Notes: The Berkowitz [2001] LR1 and LR3 statistics are used to evaluate the predictive power of RNDs and RWDs estimated under alternative models using the FTSE 100 option prices for the years 2000-2005. The forecast horizons include 1 day, 1 week, 2 weeks, 3 weeks, and 4 weeks, with the periods for all horizons being non-overlapping. Figures in parentheses refer to p-values. The RWDs are transformed from the RNDs using either parametric (betadistribution function) or non-parametric statistical calibration.

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Section: Density Predictionsupporting

confidence: 83%

Section: Risk-neutral and Real-world Densitiesmentioning

confidence: 99%

Section: Risk-neutral and Real-world Densitiesmentioning

confidence: 99%

Section: Density Predictionmentioning

confidence: 99%

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The Impact of Jump Dynamics on the Predictive Power of Option-Implied Densities

Wang¹

2009

JOD

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“…have supported the notion that option-implied volatilities and densities have a strong forecasting ability (Poon and Granger, 2003;Pong et al, 2004;Liu et al, 2007;Shackleton et al, 2010). (c) Compared with the structure model, which was proposed by Merton (1974), a model with options data may avoid capital structure assumptions.…”

Section: Introductionmentioning

confidence: 99%

Credit Spreads and Bankruptcy Information From Options Data

Tzeng

2014

Ann. Finan. Econ.

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The changes in implied bankruptcy chances are applied to explain the credit default swap (CDS) spread changes of six financial institutions during the financial crisis. I estimated the chances from options data, with the assumption that risk neutral density (RND) is composed of lognormal densities with a chance of bankruptcy. Interest rate information and market information from firm-and index-level RNDs are used to explain CDS spread changes. The empirical findings show that firm-level information provides more explanations compared with index-level information. The changes in firm-level return is a critical determinant of CDS spreads. The changes in implied bankruptcy chances are significantly and positively related to spread changes. Finally, the changes in slope term is negatively related to spread changes.

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The Volatility and Density Prediction Performance of Alternative GARCH Models

Huang

Wang

2011

Journal of Forecasting

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This study compares the volatility and density prediction performance of alternative GARCH models with different conditional distribution specifications. The conditional residuals are specified as normal, skewed-t or compound Poisson (jump) distribution based upon a nonlinear and asymmetric GARCH (NGARCH) model framework. The empirical results for the S&P 500 and FTSE 100 index returns suggest that the jump model outperforms all other models in terms of both volatility forecasting and density prediction. Nevertheless, the superiority of the non-normal models is not always significant and diminished during the sample period on those occasions when volatility experiences an obvious structural change. Volatility and Density Prediction 159Based on 10,000 repeats of simulated prices and volatility values for many rolling samples, 4 our empirical results for various forecasting horizons reveal that the return processes are better described by the non-normal specifications. Furthermore, the NGARCH-jump model is found to outperform the others in terms of both volatility forecasting and density prediction, although the achievement in the latter of these is less significant. Nevertheless, the advantages of these non-normal models on both applications are diminished for certain sample periods, in particular a period characterized by low, stable volatility. It may therefore be necessary to detect any structural changes in volatility, and to adapt to these when employing any of the historical models for time series modeling and forecasting, such as the GARCH-type models. Otherwise, a more complicated model that requires a much heavier computation load may not be superior to a simple one.The remainder of this paper is organized as follows. The three volatility models employed in this study are described in detail in the next section, followed in the third section by presentation of the measures used to evaluate the volatility forecasting and density prediction performance of the various models. The fourth section presents the data used for our empirical analysis, with the analysis subsequently being presented in the fifth section along with a discussion of the results. Finally, the conclusions drawn from this study are presented in the sixth section. EMPIRICAL MODELSMany types of GARCH models, such as the EGARCH (Nelson, 1991), NGARCH (Engle and Ng, 1993) and GJR (Glosten et al., 1993) models, are capable of capturing the asymmetric news impact that has been well documented for equity returns. As the focus of this study is on the distributional specifications of residuals (rather than the dynamic specifications of conditional variance) and the jump model we follow (Duan et al., 2006(Duan et al., , 2007 is specified for the NGARCH model, we simply use the NGARCH-normal model of Engle and Ng (1993) as the benchmark to investigate whether the NGARCH-skewed-t and the NGARCH-jump models can improve the precision of volatility and density prediction. 5 This section provides details of the specifications and estimation procedures ...

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A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

Cited by 53 publications

References 82 publications

The Impact of Jump Dynamics on the Predictive Power of Option-Implied Densities

The Impact of Jump Dynamics on the Predictive Power of Option-Implied Densities

Credit Spreads and Bankruptcy Information From Options Data

The Volatility and Density Prediction Performance of Alternative GARCH Models

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