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The Dynamics of Stochastic Volatility: Evidence from Underlying and Option Markets
, 2000
"... This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultane ..."
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Cited by 126 (3 self)
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This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultaneously. I conclude that the square root stochastic variance model of Heston (1993) and others is incapable of generating realistic returns behavior and find that the data are more accurately represented by a stochastic variance model in the CEV class or a model that allows the price and variance processes to have a timevarying correlation. Specifically, I find that as the level of market variance increases, the volatility of market variance increases rapidly and the correlation between the price and variance processes becomes substantially more negative. The heightened heteroskedasticity in market variance that results generates realistic crash probabilities and dynamics and causes returns to display values of skewness and kurtosis much more consistent with their sample values. While the model dramatically improves the fit of options prices relative to the square root process, it falls short of explaining the implied volatility smile for shortdated options.
A Study towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation
, 1999
"... The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundame ..."
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Cited by 111 (4 self)
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The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental price S t and a set of option contracts ### I it # i=1;m # where m # 1 and # I it is the BlackScholes implied volatility.We use Heston's #1993# model as an example and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show that the univariate approach only involving options by and large dominates. Abyproduct of this #nding is that we uncover a remarkably simple volatility extraction #lter based on a polynomial lag structure of implied volatilities. The bivariate approachinvolving both the fundamental and an option appears useful when the information from the cash market ...
Essays in Financial Econometrics
, 2000
"... We examine methods to extract various types of information from derivative prices by means of continuous time models and modern estimation and filtering methods. The first essay introduces the approach allowing the joint estimation of the objective and riskneutral measures based on the time series ..."
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Cited by 2 (0 self)
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We examine methods to extract various types of information from derivative prices by means of continuous time models and modern estimation and filtering methods. The first essay introduces the approach allowing the joint estimation of the objective and riskneutral measures based on the time series of assets returns and options prices in the stochastic volatility model framework. The second essay develops a model, which allows for simultaneous consideration of multiple assets and their derivatives. This model, when combined with the filtering techniques, allows for unbiased estimation of the stochastic discount factor without any initial assumptions about the utility function. The third essay extends the approach by suggesting a new class of jump diffusion models, which allows for analytical option pricing. The various estimation strategies are discussed.
Forecasting volatility under multivariate stochastic volatility via reprojection
, 1999
"... This paper evaluates the performance of volatility forecasting based on stochastic volatility (SV) models. We show that the choice of squared assetreturn residuals as proxy of expost volatility directly leads to extremely low explanatory power in the common regression analysis of volatility foreca ..."
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Cited by 1 (1 self)
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This paper evaluates the performance of volatility forecasting based on stochastic volatility (SV) models. We show that the choice of squared assetreturn residuals as proxy of expost volatility directly leads to extremely low explanatory power in the common regression analysis of volatility forecasting. We argue that since the measure of volatility is always model dependent, the performance of volatility forecasting should be evaluated in a consistent model framework. The main contributions of this paper include: First, we apply the EMM estimation method proposed by Gallant and Tauchen (1996) to estimate the multivariate SV model of asset returns; Secondly, we further implement the underlying volatility reprojection technique proposed by Gallant and Tauchen (1998) to the estimated multivariate SV model; Finally, we illustrate that the performance of volatility forecasting based on reprojected volatility series can be substantially improved. Furthermore, we show that the volatility forecasting performance based on multivariate SV model improves over the univariate SV models due to the correlated movements of asset return volatility.
Which Model for the Italian Interest Rates?
, 2002
"... In the recent years, diffusion models for interest rates became very popular. In this paper, we try to do a selection of a suitable diffusion model for the Italian interest rates. Our data set is given by the yields on threemonth BOT, from 1981 to 2001, for a total of 470 observations. We investig ..."
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In the recent years, diffusion models for interest rates became very popular. In this paper, we try to do a selection of a suitable diffusion model for the Italian interest rates. Our data set is given by the yields on threemonth BOT, from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatility models, paying more attention to affine models. Estimating diffusion models via maximum likelihood, which would lead to efficiency, is usually unfeasible since the transition density is not available. Recently it has been proposed a method of moments which gains full efficiency, hence its name of Efficient Method of Moments (EMM); it selects the moments as the scores of an auxiliary model, to be computed via simulation, thus EMM is suitable to diffusions whose transition density is unknown, but which are convenient to simulate. The auxiliary model is selected among a family of densities which spans the density space. As a byproduct, EMM provides diagnostics which are easy to compute and to interpret. We find evidence that onefactor models are rejected, while a logarithmic specification of the volatility provides the best fit to the data, in agreement with the findings on U.S. data. Moreover, we provide evidence that this model allows a more flexible representation of the yield curve.
SPECIFICATION ANALYSIS OF DIFFUSION MODELS FOR THE ITALIAN SHORT RATE
"... Abstract. In recent years, diffusion models for interest rates became very popular. In this paper, we perform a selection of a suitable diffusion model for the Italian short rate. Our data set is given by the yields on threemonth BOT (Buoni Ordinari del Tesoro), from 1981 to 2001, for a total of 4 ..."
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Abstract. In recent years, diffusion models for interest rates became very popular. In this paper, we perform a selection of a suitable diffusion model for the Italian short rate. Our data set is given by the yields on threemonth BOT (Buoni Ordinari del Tesoro), from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatility models, paying more attention to affine models. Estimating diffusion models via maximum likelihood, which would lead to efficiency, is usually unfeasible since the transition density is not available. Recently it has been proposed a method of moments which gains full efficiency, hence its name of Efficient Method of Moments (EMM); it selects the moments as the scores of an auxiliary model, to be computed via simulation, thus EMM is suitable to diffusions whose transition density is unknown, but which are convenient to simulate. The auxiliary model is selected among a family of densities which spans the density space. As a byproduct, EMM provides diagnostics which are easy to compute and to interpret. We find evidence that onefactor models and multifactor affine models are rejected, while a logarithmic specification of the volatility provides the best fit to the data.