Testing the Stability of Implied Probability Density Functions

Bliss, Robert R.; Panigirtzoglou, Nikolaos

doi:10.2139/ssrn.209650

Cited by 65 publications

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“…Another criterion of interest was suggested by Bliss and Panigirtzoglou (2002). It is to select the λ such that the maximum fitted price error is approximately equal to one half of the tick size by which the options are quoted.…”

Section: Summary Of the Resultsmentioning

confidence: 99%

“…They also applied this to smoothing the implied volatility/strike function. The smoothed implied volatility smile (SML) method considered in this paper was developed by Bliss and Panigirtzoglou (2002). The method follows Malz (1997a,b) in smoothing in implied volatility/delta space and Campa et al (1998) in using a natural spline to smooth the function.…”

Section: Smoothed Implied Volatility Smilementioning

confidence: 99%

“…For this reason, we analyze the perturbed-price RNDs by examining the distribution of certain summary statistics. Both Cooper (1999) and Bliss and Panigirtzoglou (2002) studied the mean, standard deviation, skewness, and kurtosis of their estimated RNDs, but Bliss and Panigirtzoglou (2002) examined a larger set of summary statistics which also include median-based skewness, mode-based skewness, quartile-based skewness as well as tail percentiles. It is believed that the quality of these summary statistics derived from the estimated RNDs, when taken together, reflects the quality of the entire distribution.…”

Section: Monte Carlo Experiments Based On Heston's Stochastic Volatilimentioning

confidence: 99%

“…Bliss and Panigirtzoglou (2002) discussed different types of weighting schemes and how the weighting can account for different sources of pricing errors. 5 SeeWaggoner (1997) for more discussions on variable smoothness penalties in spline regression.…”

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confidence: 99%

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Estimating option implied risk‐neutral densities using spline and hypergeometric functions

Hadri

2007

The Econometrics Journal

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Summary We examine the ability of two recent methods – the smoothed implied volatility smile method (SML) and the density functionals based on confluent hypergeometric functions (DFCH) – for estimating implied risk‐neutral densities (RNDs) from European‐style options. Two complementary Monte Carlo experiments are conducted and the performance of the two RND estimators is evaluated by the root mean integrated squared error (RMISE) criterion. Results from both experiments show that the DFCH method outperforms the SML method for the overall quality of the estimated RNDs concerning both accuracy and stability. An application of the two methods to the OTC currency options market is also presented.

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Section: Summary Of the Resultsmentioning

confidence: 99%

Section: Smoothed Implied Volatility Smilementioning

confidence: 99%

Section: Monte Carlo Experiments Based On Heston's Stochastic Volatilimentioning

confidence: 99%

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confidence: 99%

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Estimating option implied risk‐neutral densities using spline and hypergeometric functions

Hadri

2007

The Econometrics Journal

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“…This is consistent with the finding of Taylor et al (2010) for individual stock options that ATM implied volatility performs better than the model-free volatility expectation for the majority of their sample firms and the S&P 100 index. We also conclude that the smoothing procedure in Bliss and Panigirtzoglou (2002) can improve the performance of the model-free volatility expectation.…”

Section: Discussionmentioning

confidence: 67%

Investigating the Information Content of the Model‐Free Volatility Expectation by Monte Carlo Methods

Zhang¹,

Taylor

Wang

2012

Journal of Futures Markets

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We explore the impact of both the number of option prices and the measurement errors in option prices upon the information content of the model‐free volatility expectation, and compare it with the Black–Scholes at‐the‐money (ATM) implied volatility. We simulate the realized volatility process and option prices using Heston's price dynamics and option valuation formula. The results show that the model‐free volatility expectation always contains important information about future realized volatilities. When the option prices contain random measurement noise, the informational efficiency of the model‐free volatility expectation increases monotonically with the number of out‐of‐the‐money options. The model‐free volatility expectation outperforms the ATM implied volatility, except when there are only a few option price observations. For the traded strikes for S&P 500 index options, we further show that fitting implied volatility curves before applying the current CBOE procedure for constructing the VIX index can improve the VIX's efficiency when forecasting future realized volatilities.

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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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Testing the Stability of Implied Probability Density Functions

Cited by 65 publications

References 0 publications

Estimating option implied risk‐neutral densities using spline and hypergeometric functions

Estimating option implied risk‐neutral densities using spline and hypergeometric functions

Investigating the Information Content of the Model‐Free Volatility Expectation by Monte Carlo Methods

The Volatility and Density Prediction Performance of Alternative GARCH Models

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