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Modern multivariate control charts that use spatial signed rank are sensitive to the detection of small shifts under non-normal or gamma distributions. In this paper, Monte Carlo simulation is used to compare the performances of multivariate control charts based on the average run length. The results show that the spatial signed-rank multivariate exponentially weighted moving average (SSRM) control chart outperforms the multivariate exponentially weighted moving average (MEWMA) control chart, the double-MEWMA control chart, and the spatial signed-rank double multivariate exponentially weighted moving average control chart when detecting small shifts in the process mean. SSRM is appropriate for data from a non-normal distribution, which is valuable for the manufacturing industry when detecting waste. Moreover, SSRM is an excellent method suitable for most industrial processes, and therefore, is a very powerful tool.

The two-stage abrupt strain path change method is used to investigate the subsequent yield surface evolution, as predicted by associated J2 plasticity models. Experimental results from the literature have revealed several specificities of the yield surface evolution following such a strain-path change, including formation of a vertex and apparent non-normality. The current study showed that some features of this behavior can be simulated using models based on associated plasticity. Kinematic hardening had the most important effect, together with rate sensitivity and elasticity. The results suggest that some apparent violation of the normality condition can result from the combined effects of kinematic hardening, rate sensitivity and elasticity, even when the normality rule is built into the model.

Infrared Thermography has been used in the medical field to diagnose illnesses that produce temperature variations. Furthermore, comparisons between the temperatures of contralateral regions or patients and healthy people are used as thermography diagnostic criteria. Under both approaches, the difference in temperature is calculated and, if it falls outside normal ranges, it is considered a sign and symptom of illness. In previous works, the thermal patterns of healthy individuals have been determined in populations from Finland, Portugal, Taiwan, Brazil, and Mexico. However, a comparison of such patterns reveals meaningful discrepancies since the emissivity of the human skin depends on ethnic characteristics and age. Thus, it is necessary to estimate thermal patterns in healthy people from each population and calculate the maximum and minimum temperature differences in their contralateral regions. Specifically, the thermal patterns of healthy Colombian people have not been established so far. Therefore, this work aims to define the thermal patterns of the population of Medellin-Colombia. Such patterns can later be used as reference values to diagnose illnesses in different hospitals in the city. Thirty-seven healthy individuals participated in this study. Data was acquired from the anterior, posterior, right, and left side of the body using a FLIR A655SC thermal camera, and the acquisition protocol was defined in accordance with the method of previous work. The camera recorded twenty-four thermograms from each subject, which were segmented by region-growing and a grid mask algorithm, thus obtaining 43 regions of interest (ROI). The mean temperature and standard deviations of each ROI were also calculated. In most regions, the mean temperature varied between 31.16 °C and 34.58 °C. The lowest mean temperature and highest variability were found in acral regions. Independent samples were assumed in the statistical analysis, and the normality of the temperature of each ROI was verified by the Shapiro–Wilk test. Moreover, Student’s t-test and Mann–Whitney U test were used in the comparison of temperatures of contralateral regions with normal and non normal distributions, respectively. Finally, the temperature difference was found to be insignificant.

This paper answers a common regression misconception regarding the distribution of the predicted variable of a regression model. Adding to the confusing is the assumption that normally distributed error terms necessarily must come from normally distributed predicted variables. In this article, we use a predicted variable with a bi-modal distribution to show how normality of the predicted variable is not necessary for normally distributed error terms.

A classifier for two or more samples is proposed when the data are high-dimensional and the distributions may be non-normal. The classifier is constructed as a linear combination of two easily comp ...

A method is presented for dynamic determination of the operating reserve requirement in power systems with high wind penetration, by considering the non-normal nature of wind power uncertainty and variability as well as their stochastic dependence on the wind power forecast. Distinct from previous methods, a generalised approach is proposed to characterise the probability density of wind power uncertainty and variability at distinct wind power forecast levels. As an illustration, the approach is applied in Ireland to determine the required operating reserve at different time scales within hourly scheduling periods to meet a certain reliability level. Statistical analysis indicates that the results are sensitive to normality and independence assumptions generally adopted in previous studies, and such assumptions may lead to under/over-estimation of the required operating reserve. Thus, the proposed method, which is not based on these limiting assumptions, emerges as a more realistic solution to define operating reserve targets dynamically. It further provides insight for planning studies and the operation of power systems with high wind power penetration.

This paper presents a general numerical scheme for the fractional plastic flow rule, dedicated to a wide class of materials manifesting the non-normality of plastic flow and induced plastic anisotropy. To determine the vector of the plastic flow, a special numerical procedure has been developed, which is applicable for any smooth and convex yield function. The obtained approximation is verified based on an analytical solution. The paper also presents a set of numerical results for the generalised Drucker–Prager model.

The study of capability of measurement processes is becoming a common practice within Quality Management Systems. Actually, “Gauge R&R study” techniques are currently largely widespread. In general, most of the tools described in the scientific literature, prescribed by the international standards and/or implemented in practical applications are based on the normality assumption of data distributions. This work discusses some alternative approaches for “gauge R&R study” when non-normal data distributions are involved. In order to clarify the impact of this problem in practical applications, the techniques considered in the present paper are analyzed through computer simulation of real case studies in the field of dimensional tolerancing.

Non-inferiority trials are becoming very popular for comparative effectiveness research. These trials are required to show that the effect of an experimental treatment is not worse than that of a reference treatment by more than a specified margin. Hence non-inferiority trials are of great importance, when superiority cannot be claimed. A three-arm non-inferiority trial consists of a placebo, a reference treatment, and an experimental treatment is considered. However unlike the traditional choices, it is assumed that the distributions of the end points corresponding to these treatments are unknown and suggested test procedures for a three-arm non-inferiority trial based on monotone transformations in conjunction with a normal approximation. The resulting test procedures are flexible and robust. Theoretical properties of the proposed methods are also investigated. The performance of the suggested test procedures is compared to their counterparts using simulations. In terms of type I error and power, the proposed methods perform better than their counterparts in most cases. The usefulness of the proposed methods is further illustrated through an example.

We introduce a principal components model for securities' returns. The components are non-normal, exhibiting significant skewness and kurtosis. The model can explain a large proportion of the variance of the securities' returns with only one or two components. Third and higher-order components individually contribute so little that they can be considered to be noise terms.

In a linearly stable but nonlinearly unstable thermoacoustic system, thermoacoustic instability may be triggered by small-amplitude acoustic perturbation undergoing transient growth. The present work study the effect of entropy waves on transient energy growth of acoustic disturbances in triggering thermoacoustic instability. For this, modal and non-normality analysis of these thermoacoustic systems is performed first. It is shown that the systems are non-normal due to the non-orthogonality of the entropy modes and the acoustic modes. The contribution to the non-orthogonality of the acoustic modes is identified to consist of (1) the non-trivial boundary conditions, (2) unsteady heat release and (3) the mean flow present. To quantify the amplification of the energy of the acoustic disturbances, transient growth is characterized and calculated. It is found that the initial acoustic energy can be amplified by a factor of the order of 103, if the system is ended with choked outlet. It is 2-order greater than the G ac max (100–101) observed in the open-ended thermoacoustic system. Such dramatic amplification is mainly due to the energy transfer occurred at the system outlet from entropy to acoustic modes. The detailed analysis reveals that the entropy waves in the choked system have much greater potential to trigger thermoacoustic instability than expected. Neglecting the entropy waves might lead to wrong prediction of the transient growth of acoustic disturbances in triggering thermoacoustic instability.

Aging water mains systems are becoming a growing concern for maintenance. The structural deterioration of water mains is affected by different factors such as pipe age, pipe material, soil condition, pipe size, climate condition among others. Since pipes are underground and obtaining data for pipes are difficult and expensive to obtain, various statistical modeling methods have been used to analyze the factors contributing to the pipe condition deterioration and predict the failure of pipes. This paper applies copula method for pipe data analysis. Copula is an emerging method of modeling that has been widely used in financial sectors. There has been recent use in hydrology and bridge management sectors but the method has not been applied to other civil engineering disciplines. Copula method is very useful where marginals belong to different families of distributions. This paper uses copula modeling to determine dependency between several variables of pipe condition and compare how it may be a better choice for determining correlation dependency for data which are non normal and skewed. Copula modeling is used in this paper to predict pipe leakage due to climate condition, in which water temperature is used as a factor. Vine copula is used to develop multi variable simulation models for pipe data. Copula method is very useful and provides better results where marginals belong to different families of distributions, which is observed in the data set used for pipe data analysis.

Thermoacoustic instability occurs in many practical combustion systems. These systems are non-normal and associated with transient growth of acoustic disturbances. If the transient growth is large enough, then thermoacoustic instability may be triggered. In this work, transient energy growth analysis of a thermoacoustic system with a choked outlet is conducted. The effect of the choked boundary is studied by using an analytical and a linearized Euler equation (LEE) method. To quantify the transient growth, two energy measures are defined and calculated. One is associated with the acoustical energy. The other is the total energy of both entropy and acoustic fluctuations. Comparison is made between the transient growth results obtained from the analytical method and those from the LEE method. It is found that the transient growth analysis of the total energy by using the analytical model with the expression of the choked outlet is consistent with that by using the LEE method. However, when only acoustical energy is considered, the analytical model may leads to a wrong prediction of transient growth. The present work opens up new applicable way to predict transient stability behaviors of a practical engine system ended with a choked outlet.

The granular soils are pressure dependent materials and substantial volume change occurs during loading. Some granular soils contract (volume decrease) when sheared and some dilate (volume increase), depending on their initial state. Owing to the plastic volume change that accompanied plastic deformation, the lack of normality rule arises and the granular soil exhibits a non-associated flow rule. As known the non normality has destabilizing effect on the soil behavior in the hardening regime (loss of positive definiteness of the second order work). The unstable behavior usually develops in association with dilation. A contracting soil displaying hardening and stable material behavior under drained conditions, may succumb to unstable flow type when its behavior becomes dilating. This paper deals with the extension of the static shakedown theorem to dilative granular soils in drained conditions, exhibiting pre-failure instability in the hardening regime, in the framework of non associated plasticity.

We generalize existing structural credit risk models that account for contagion effects across economic sectors, to capture the impact of neglected skewness and excess kurtosis in the asset return process, on the shape of the credit loss distribution. We specify Skew-Normal and Skew-Student t densities for the underlying asset return process and estimate the derived credit loss density using sector default rates based on proprietary data from the Central Bank of Mexico for six firm sectors. We show that, out of the six sectors analyzed, there is a significant contagion effect in ‘Commerce’, ‘Services’ and ‘Transport’. Moreover, we show that the non-Gaussian modelling of the common factor provides a better characterization than its Gaussian counterpart for the ‘Services’ sector. This result has a significant impact on the shape and the corresponding Value-at-Risk levels of the ‘Services’ credit loss distribution. In this context, traditional Basel and vendor-based credit risk models are inadequate as these do not consider the individual or the joint impact of contagion and non-Gaussian asset returns.

We provide several examples concerning extensions of real-valued functions on countable closed discrete subsets of products N ω 1 or N 2 ω of natural numbers over the whole products.

Two projective subvarieties of P r are said to be projectively equivalent if they are identified by a coordinate change. Up to projective equivalence, varieties of minimal degree were completely classified more than one hundred years ago by P. del Pezzo and E. Bertini. As the next case, we study the same problem for del Pezzo varieties, focusing on the non-normal case of degree ⩾5. Note that the cases of degrees 3 and 4 were dealt with in Lee et al. (2011) [8] and Lee et al. (2012) [9] , respectively. Our main result, Theorem 4.1, provides a complete classification of non-normal del Pezzo varieties of degree at least 5, up to projective equivalence.

In this article, we consider the problem of testing the equality of mean vectors of dimension p of several groups with a common unknown non-singular covariance matrix @S, based on N independent observation vectors where N may be less than the dimension p. This problem, known in the literature as the multivariate analysis of variance (MANOVA) in high-dimension has recently been considered in the statistical literature by Srivastava and Fujikoshi (2006) [8], Srivastava (2007) [5] and Schott (2007) [3]. All these tests are not invariant under the change of units of measurements. On the lines of Srivastava and Du (2008) [7] and Srivastava (2009) [6], we propose a test that has the above invariance property. The null and the non-null distributions are derived under the assumption that (N,p)->~ and N may be less than p and the observation vectors follow a general non-normal model.

We generalize A.H. Stoneʼs witnesses to the non-normality of N ω 1 and produce new strong witnesses to the non-normality with a pair of disjoint countable closed discrete sets that fail to have an open separation by open sets having disjoint closures. Our generalization of A.H. Stoneʼs witnesses yields among other things that all closed subsets of N ω 1 with non-Lindelof boundaries fail to have an open separation with a closed disjoint homeomorphic copy of themselves.

Standard quantitative portfolio analysis techniques, including mean-variance analysis, historical risk and performance estimation, and various portfolio optimization techniques, implicitly require all assets under consideration having the same length of return histories. Unfortunately, it is often the case that certain assets have shorter return histories than others. We present a method, which is a significant improvement over an existing technique, for efficiently backfilling missing returns while accounting for non-normal distributions.

Results of the first dispersion analyses of polarized reflection spectra from a monoclinic a – c crystal plane taking properly into account the monoclinic symmetry and non-normal incidence on the crystal surface are reported. Spectra were recorded for the incidence angles α = 8°, 16°, 40° and 60°, and for each at four different polarization angles. For the first two incidence angles the spectra were additionally analyzed under the assumption of normal incidence and the results were compared to those which resulted from the exact treatment. The comparison focused on two different aspects. The first aspect concerns the validity of the oscillator parameters. Accordingly, oscillator parameters of IR active modes obtained by dispersion analysis under the assumption of normal incidence do not show systematic errors despite the simplified treatment. This is a consequence of the fact that errors due to the incorrect assumption of normal incidence are compensated mainly by increases of the diagonal terms of the high frequency dielectric tensor. The corresponding values obtained under the assumption of normal incidence show averaged standard deviations of about 2% at 8° and about 9% at 16°. The second aspect investigated focuses on the employment of the oscillator parameters to generate the dielectric function tensor for optical calculations. Here we found that, as a direct consequence of the increased high frequency dielectric tensor, errors substantially increase if the resulting dielectric tensor functions are employed to calculate the reflectance at higher angles of incidence. Therefore, and since the increase of computational effort due to the exact treatment is small, we strongly suggest and encourage its use instead of the simplified treatment.

In this article we study the classification of non-normal cubic hypersurfaces over an algebraically closed field K of arbitrary characteristic. Let X ⊂ P K r be an irreducible non-normal cubic hypersurface. If r ≥ 5 , then X is necessarily a cone (Remark 2.3). In view of this fact it suffices to classify irreducible non-normal cubic hypersurfaces X ⊂ P K r for r ≤ 4 . We prove that there are precisely five non-normal cubic equations (resp. six non-normal cubic equations) when char K ≠ 2 , 3 (resp. when char K is either 2 or 3), up to projective equivalence. Also we describe the normalization of X in detail.

This paper, using a threshold vector error-correction (TVECM) model, examines whether BRENT crude spot and futures oil prices are cointegrated. By employing this methodology we are able to evaluate the degree and dynamics of transaction costs resulting from various market imperfections. TVECM model is applied on daily spot and futures oil prices covering the period 1990–2009. The hypothesis we test is to what extent BRENT crude is indeed an integrated oil market in terms of threshold effects and adjustment costs. Our findings support that market follows a gradual integration path. We find that BRENT crude spot and futures are cointegrated, though two regimes are clearly identified. This implies that a threshold exists and it is indeed significant. Adjustment costs in the error correction are present, and they are valid at the typical regime that is the dominant, and as a result should not be ignored.

We distinguish non-normality from non-linearity in G7 real exchange rate dynamics by correcting the critical values of the Kapetanios et al. [Kapetanios, G., Shin, Y., Snell, A., 2003. Testing for a unit root in the non-linear STAR framework. Journal of Econometrics, 112, 359–379] test for non-normality using the wild bootstrap. Our findings validate non-linear Purchasing Power Parity net of non-normality effects.

We test for Purchasing Power Parity (PPP) in the G7 area for the post-Bretton Woods period. Unlike previous studies, we correct the critical values of the standard unit root test using a wild bootstrap technique. Our findings reject PPP, thus enhancing the contribution of the recent non-linear PPP literature.

Most studies employing ARCH and GARCH models document the existence of severe excess kurtosis in the estimated residuals. This non-normality may be due to model misspecifications, structural changes, or outliers. We conduct simulation experiments to examine the impact of extreme observations on the estimated parameters and residuals in the ARCH models. Then, we propose an iterative algorithm to detect and correct for the non-normality generated by extreme observations and additive outliers. Results for the simulated data, US equity returns and $/£ exchange rates are presented. Correcting outliers dramatically reduces the non-normality and bias in the estimated coefficients for small samples.

A Cayley graph X = Cay(G, S) of group G is said to be normal if R(G) is normal in Aut(X). Let G = «a, b | an = b2 = 1 », S be a generating set of G, |S| = 4. In this paper we show that any one-regular and 4-valent Cayley graph X = Cay(G, S) of dihedral groups G is normal except that n = 4s, and X ≃ Cay(G, {a, a-1, aib, a-ib}), where i2 ≡ ± 1 (mod 2s), 2 ≤ i ≤ 2s - 2.

For linear mixed models, Lange and Ryan's plot [Lange, N., Ryan, L., 1989. Assessing normality in random effects models. Ann. Statist. 17, 624–642] was derived for diagnosing random effect distributions. We show it is sensitive to both non-normality of random effects and mis-specified mean models, and thus may be more useful as a general diagnostic.

By employing the wild bootstrap we calculate the ‘correct’ size of the relevant test statistics for the test of the null hypothesis of efficiency in betting markets. Our findings are that the overall conclusion of the rejection of the null hypothesis is still valid.

Resume Nous etudions la destabilisation des couches de melange etirees en examinant l'influence sur l'instabilite de Kelvin–Helmholtz d'un champ de vitesse hyperbolique. Dans ce cas, l'ecoulement de base est instationnaire. Nous etudions l'evolution temporelle des perturbations dans un cadre non-visqueux a l'aide d'une approche de type non normal. On calcule l'amplification maximale pour chaque instant. Cette etude met en evidence l'effet stabilisateur (resp. destabilisateur) d'une compression (resp. d'un etirement) meme pour un faible taux de compression (resp. d'etirement). Pour citer cet article : T. Gomez, M. Rossi, C. R. Mecanique 331 (2003).

Carlson and Parkin [Economica 42 (1975) 123] quantify qualitative survey data on expectations assuming aggregate expectations are normally distributed. Using UK survey data we find normal distributions provide as accurate expectations of inflation and output growth as any permitted non-normal alternative.

With the advent in recent years of large financial data sets, machine learning and high-performance computing, analysts can backtest millions (if not billions) of alternative investment strategies. Backtest optimizers search for combinations of parameters that maximize the simulated historical performance of a strategy, leading to backtest overfitting.The problem of performance inflation extends beyond backtesting. More generally, researchers and investors tend to report only positive outcomes, a phenomenon known as selection bias. Not controlling for the number of trials involved in a particular discovery leads to over-optimistic performance expectations.The Deflated Sharpe Ratio (DSR) corrects for two leading sources of performance inflation: Selection bias under multiple testing and non-Normally distributed returns. In doing so, DSR helps separate legitimate empirical findings from statistical flukes.

This paper describes an erosion study, which examines the effect of impact angle on the erosion behaviour of diamond coatings deposited on tungsten substrates by chemical vapour deposition (CVD). The coatings were 37–60 ?m in thickness and were erosion tested using angular silica sand with a mean diameter of 194 ?m at a particle velocity of 268 m s?1. The impact angles used were 30, 45, 60 and 90°. The results show that the damage features, termed "pin-holes" are generated at all angles, though the number of impacts required for pin-hole initiation is significantly increased at lower angles. This work provides useful information in attempting to explain the mechanism by which damage is generated during the high velocity sand erosion of CVD diamond.

We report simulations, using actual stock return data, of statistical tests of long-horizon buy-and-hold stock returns. We use benchmark portfolios purged of new-listings and rebalancing biases, and find that many proposed tests are misspecified, due in part to skewness. The use of a single control firm instead of a portfolio still produces misspecification, particularly in large samples. We document an inverse relation between skewness bias and sample size, and also document an overlapping-horizons bias. Both biases worsen as the holding period lengthens. Due to interacting biases, tests can be well-specified in one testing scenario but not another, seeming similar, one. A two groups test applied to winsorized abnormal returns exhibits correct specification and considerable power most often in among the tests simulated.

The simulation of random velocity and pressure signals at un-instrumented locations of a structure conditioned on measured records is often needed in wind engineering. Malfunctioning equipment may leave a hole in a wind data set or information may be lacking due to a limited number of instruments or difficulty in monitoring at certain locations. This paper presents a non-Gaussian conditional simulation technique in the context of non-Gaussian pressure fluctuations in separated flow regions, or velocity fluctuations in atmospheric flows. First, a uni-variate non-Gaussian simulation technique is developed. This is extended to multi-variate, and subsequently utilized as a mapping technique in a conditional simulation algorithm. This technique is applied to both the extension of existing records beyond recorded lengths, and the simulation of missing or damaged records based on measured data at other locations.

Process capability indices C p ( u , v ), which include the four basic indices C p , C pk , C pm and C pmk as special cases, have been proposed to measure process potential and performance. C p ( u , v ) are appropriate indices for processes with normal distributions, but have been shown to be inappropriate for processes with non-normal distributions. In this paper, we first consider two generalizations of C p ( u , v ), which we refer to as C Np ( u , v ) and C ′ Np ( u , v ), to cover cases where the underlying distributions may not be normal. Comparisons between C Np ( u , v ) and C ′ Np ( u , v ) are provided. The results indicated that the generalizations C Np ( u , v ) are superior to C ′ Np ( u , v ) in measuring process capability. We then present a case study on an aluminum electrolytic-capacitor manufacturing process to illustrate how the generalizations C Np ( u , v ) may be applied to actual data collected from the factories.

Given two sources of forecasts of the same quantity, it is possible to compare prediction records. In particular, it can be useful to test the hypothesis of equal accuracy in forecast performance. We analyse the behaviour of two possible tests, and of modifications of these tests designed to circumvent shortcomings in the original formulations. As a result of this analysis, a recommendation for one particular testing approach is made for practical applications.

The present article considers the linear ultrastructural model which encompasses the two popular forms of measurement error models, viz., the functional and structural models. The measurement error variance associated with the explanatory variable is assumed to be known which leads to consistent estimators of parameters. The efficiency properties of the thus obtained estimators of slope parameter, intercept term and the measurement error variance of study variable are derived under non-normal error distributions and the effects of departures from symmetry and peakedness of the error distributions are studied.

The Cornish-Fisher expansion is a popular method to adjust value-at-risk calculations for the skewness and kurtosis of non-normal return distribution. On the other hand, it is an open secret that “modified value-at-risk” calculations produce “strange” results from time to time, under certain parameter constellations. But the phenomenon was poorly understood, and no guidance was available from academia. In this research note, we illustrate the shortcomings of the traditional Cornish-Fisher expansion, by analyzing the distribution of S&P 500 price returns. We apply insights from recent research, which turns the Cornish-Fisher expansion into a well-behaved and accurate tool for modelling empirical non-normal return distributions.

A comprehensive empirical evaluation is presented of the sensitivity to non-normality of the main tests for individual effects in a one-way error components panel data model.

For any natural number g ≥ 2, and for any odd prime p not dividing g, we give an explicit example of a ring R of real numbers with the Following three properties: • is uncountable, • all numbers ∈ , ≠ 0, are normal to base , and • all numbers ∈ are non-normal to base · . This result contains, e.g., explicitly given numbers x such that, for any non-constant polynomial q ∈ Z[x], the number q(x) is normal to base 3 but non-normal to base 15.

Suppose that X is a Cohen-Macaulay monomial variety with injective normalisation the weighted projective space P rk(m, 1, . . . , 1) for m ≥ 1. Then D ( X ) M D ( P rk(m, 1, . . . , 1)) if and only if X is D -affine if and only if Hr( X , O X ) = 0. We also show that such varieties exist (for r ≥ 2) and give a combinatorial condition which precisely specifies them.

In this paper we have provided a general result on the higher-order approximate moments of the ratio of quadratic forms in the non-normal vector. The results for the normal case are then presented as a special case of this result. It is also indicated that the results for a large class of econometric estimators and test statistics can be obtained by using our general result.

The non-normality of Wilson-type lattice Dirac operators has important consequences - the application of the usual concepts from the textbook (hermitian) quantum mechanics should be reconsidered. This includes an appropriate definition of observables and the refinement of computational tools. We show that the truncated singular value expansion is the optimal approximation to the inverse operator D^{-1} and we prove that due to the gamma_5-hermiticity it is equivalent to gamma_5 times the truncated eigenmode expansion of the hermitian Wilson-Dirac operator., Comment: Lattice2001(theorydevelop)

Based on the theory of a wedge between the physical and risk-neutral conditional volatilities in Christoffersen, Elkamhi, Feunou, and Jacobs (2009), we develop a modification on the GARCH option pricing model with the filtered historical simulation proposed in Barone-Adesi, Engle, and Mancini (2008). The current conditional volatilities under the physical and risk-neutral measures are the same in the previous model, but should have been allowed to be different. Using an extensive data on S&P 500 index options, our approach, which employs the current risk-neutral conditional volatility estimated from the cross-section of the option prices (in contrast to the existing GARCH option pricing models), maintains theoretical consistency under conditional non-normality as well as improves the empirical performances. Remarkably, the risk-neutral volatility dynamics are stable over time under this model. In addition, the comparison between the VIX index and the risk-neutral integrated volatility validates our approach economically.