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81
On the Detection and Estimation of Long Memory in Stochastic Volatility
, 1995
"... Recent studies have suggested that stock markets' volatility has a type of longrange dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing ..."
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Cited by 207 (6 self)
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Recent studies have suggested that stock markets' volatility has a type of longrange dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing this longrange dependence are examined and the properties of a LongMemory Stochastic Volatility (LMSV) model, constructed by incorporating an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process in a stochastic volatility scheme, are discussed. Strongly consistent estimators for the parameters of this LMSV model are obtained by maximizing the spectral likelihood. The distribution of the estimators is analyzed by means of a Monte Carlo study. The LMSV is applied to daily stock market returns providing an improved description of the volatility behavior. In order to assess the empirical relevance of this approach, tests for longmemory volatility are described and applied to an e...
Maximum likelihood estimation for stochastic volatility models
 JOURNAL OF FINANCIAL ECONOMICS
, 2007
"... We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure ..."
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Cited by 106 (3 self)
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We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a shortdated atthemoney option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.
Estimation methods for stochastic volatility models: a survey
 Journal of Economic Surveys
, 2004
"... The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome ..."
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Cited by 45 (2 self)
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The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome this problem, being at the same time, empirically feasible. As a consequence, several extensions of the SV models have been proposed and their empirical implementation is increasing. In this paper, we review the main estimators of the parameters and the volatility of univariate SV models proposed in the literature. We describe the main advantages and limitations of each of the methods both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.
Nonlinear and NonGaussian StateSpace Modeling with Monte Carlo Techniques: A Survey and Comparative Study
 In Rao, C., & Shanbhag, D. (Eds.), Handbook of Statistics
, 2000
"... Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or nonGaussian state estimation problems have been developed. Numerical integration becomes extremely computerintensive in the higher dimensional cases of the state vect ..."
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Cited by 22 (4 self)
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Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or nonGaussian state estimation problems have been developed. Numerical integration becomes extremely computerintensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling techniques such as Monte Carlo integration with importance sampling, resampling, rejection sampling, Markov chain Monte Carlo and so on are utilized, which can be easily applied to multidimensional cases. Thus, in the last decade, several kinds of nonlinear and nonGaussian filters and smoothers have been proposed using various computational techniques. The objective of this paper is to introduce the nonlinear and nonGaussian filters and smoothers which can be applied to any nonlinear and/or nonGaussian cases. Moreover, by Monte Carlo studies, each procedure is compared by the root mean square error criterion.
Stochastic Volatility, Smile & Asymptotics
, 1998
"... We consider the pricing and hedging problem for options on stocks whose volatility is a random process. Traditional approaches, such as that of Hull & White, have been successful in accounting for the much observed smile curve, and the success of a large class of such models in this respect is g ..."
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Cited by 17 (9 self)
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We consider the pricing and hedging problem for options on stocks whose volatility is a random process. Traditional approaches, such as that of Hull & White, have been successful in accounting for the much observed smile curve, and the success of a large class of such models in this respect is guaranteed by a theorem of Renault & Touzi, for which we present a simplified proof. We also present new asymptotic formulas that describe the geometry of smile curves and can be used for interpolation of implied volatility data. Motivated by the robustness of the smile effect to specific modelling of the unobserved volatility process, we present a new approach to stochastic volatility modelling starting with the BlackScholes pricing PDE with a random volatility coefficient. We identify and exploit distinct time scales of fluctuation for the stock price and volatility processes yielding an asymptotic approximation that is a BlackScholes type price or hedging ratio plus a Gaussian random variable quantifying the risk from the uncertainty in the volatility. These lead us to translate volatility risk into pricing and hedging bands for the derivative securities, without needing to estimate the market's value of risk. For some special cases, we can give explicit formulas. We outline
The Impact Of Energy Derivatives On The Crude Oil Market
, 1999
"... We examine the effects of energy derivatives trading on the crude oil market. There is a common public and regulatory perception that derivative securities increase volatility and can have a destabilizing effect on the underlying market. Consistent with this view, we find an abnormal increase in vol ..."
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Cited by 13 (0 self)
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We examine the effects of energy derivatives trading on the crude oil market. There is a common public and regulatory perception that derivative securities increase volatility and can have a destabilizing effect on the underlying market. Consistent with this view, we find an abnormal increase in volatility for three consecutive weeks following the introduction of NYMEX crude oil futures. While there is also evidence of a longerterm volatility increase, this is likely due to exogenous factors such as the continuing deregulation of the energy markets. Subsequent introductions of crude oil options and derivatives on other energy commodities have no effect on crude oil volatility. We also examine the effects of derivatives trading on the depth and liquidity of the crude oil market. This analysis reveals a strong inverse relation between the open interest in crude oil futures and spot market volatility. Specifically, when open interest is greater, the volatility shock associated with a giv...
Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates
, 2000
"... This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate t ..."
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Cited by 11 (0 self)
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This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model’s performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or “leverage effect ” does help to explain the skewness of the volatility “smile”, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino & Turnbull (1990), our empirical findings strongly suggest the existence of a nonzero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the
Consequences for option pricing of a long memory in volatility. Unpublished Manuscript. Department of Accounting and Finance
, 2000
"... The economic consequences of a long memory assumption about volatility are documented, by comparing implied volatilities for option prices obtained from short and long memory volatility processes. Numerical results are given for options on the S & P 100 index from 1984 to 1998, with lives up to ..."
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Cited by 11 (0 self)
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The economic consequences of a long memory assumption about volatility are documented, by comparing implied volatilities for option prices obtained from short and long memory volatility processes. Numerical results are given for options on the S & P 100 index from 1984 to 1998, with lives up to two years. The long memory assumption is found to have a significant impact upon the term structure of implied volatilities and a relatively minor impact upon smile effects. These conclusions are important because evidence for long memory in volatility has been found in the prices of many assets.