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41
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 this ..."
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Cited by 125 (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 48 (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.
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 16 (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 guara ..."
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Cited by 13 (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
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 two ..."
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Cited by 8 (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.
Stochastic Volatility
 Statistics in Finance. Applications of Statistics Series
, 1996
"... The volatility of a financial asset is the variance per unit time of the logarithm of the price of the asset. Volatility has a key role to play in the determination of risk and in the valuation of options and other derivative securities. The widespread BlackScholes model for asset prices assumes co ..."
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Cited by 6 (0 self)
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The volatility of a financial asset is the variance per unit time of the logarithm of the price of the asset. Volatility has a key role to play in the determination of risk and in the valuation of options and other derivative securities. The widespread BlackScholes model for asset prices assumes constant volatility. The purpose of this chapter is to review the evidence for nonconstant volatility and to consider the implications for option pricing of alternative random or stochastic volatility models. We concentrate on continuous time diffusion models for the volatility, but we also make comments about certain classes of discrete time models, such as ARV, ARCH and GARCH. 1 Volatility and the need for Stochastic Volatility models 1.1 Introduction A common approach in the modelling of financial assets is to assume that the proportional price changes of an asset form a Gaussian process with stationary independent increments. The celebrated (and ubiquitous) BlackScholes option pricin...
Pricing stock options under stochastic volatility and stochastic interest rates with efficient method . . .
, 1998
"... ..."
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 5 (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...