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109
Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then des ..."
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Cited by 148 (2 self)
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We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
TimeChanged Lévy Processes and Option Pricing
, 2002
"... As is well known, the classic BlackScholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to nonnormal return innovations. Second, return ..."
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Cited by 89 (12 self)
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As is well known, the classic BlackScholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to nonnormal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that timechanged Lévy processes be used to simultaneously address these three facets of the underlying asset return process. We show that our framework encompasses almost all of the models proposed in the option pricing literature. Despite the generality of our approach, we show that it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.
Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance
, 1999
"... A common model for security price dynamics is the continuous time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the BlackScholes price with the forward integrated variance replacing the BlackScholes va ..."
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Cited by 64 (3 self)
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A common model for security price dynamics is the continuous time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the BlackScholes price with the forward integrated variance replacing the BlackScholes variance. Implementing the Hull and White characterization requires both estimates of the price dynamics and the conditional distribution of the forward integrated variance given observed variables. Using daily data on closetoclose price movement and the daily range, we find that standard models do not fit the data very well and a more general three factor model does better, as it mimics the longmemory feature of financial volatility. We develop techniques for estimating the conditional distribution of the forward integrated variance given observed variables. 1 Introduction This paper has two objectives: The first is to extend and implement methods for estimating diffusion models of secu...
The Finite Moment Log Stable Process and Option Pricing
, 2002
"... We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharpl ..."
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Cited by 51 (9 self)
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We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.
Limit theory for the sample autocorrelations and extremes of a GARCH(1,1) process
, 1998
"... The asymptotic theory for the sample autocorrelations and extremes of a GARCH(1; 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close to one, i.e. when one is close to an infinite variance marginal distribution. This situation has been ..."
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Cited by 45 (9 self)
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The asymptotic theory for the sample autocorrelations and extremes of a GARCH(1; 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close to one, i.e. when one is close to an infinite variance marginal distribution. This situation has been observed for various financial logreturn series and led to the introduction of the IGARCH model. In such a situation the sample autocorrelations are unreliable estimators of their deterministic counterparts for the time series and its absolute values, and the sample autocorrelations of the squared time series have nondegenerate limit distributions. We discuss the consequences for a foreign exchange rate series. AMS 1991 Subject Classification: Primary: 62P20 Secondary: 90A20 60G55 60J10 62F10 62F12 62G30 62M10 Key Words and Phrases. GARCH, sample autocorrelations, stochastic recurrence equation, Pareto tail, extremes, extremal index, point processes, foreign exchange rates 1 Introduc...
NonStationarities in Financial Time Series, the Long Range Dependence and the IGARCH Effects
 Review of Economics and Statistics
, 2002
"... In this paper we give the theoretical basis of a possible explanation for two stylized facts observed in long logreturn series: the long range dependence (LRD) in volatility and the integrated GARCH (IGARCH). Both these eects can be theoretically explained if one assumes that the data is nonsta ..."
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Cited by 36 (5 self)
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In this paper we give the theoretical basis of a possible explanation for two stylized facts observed in long logreturn series: the long range dependence (LRD) in volatility and the integrated GARCH (IGARCH). Both these eects can be theoretically explained if one assumes that the data is nonstationary.
What Type of Process Underlies Options? A Simple Robust Test
, 2002
"... We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of atthemoney and outofthemoney options as the option maturity approaches zero. We show that these prices converge to ze ..."
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Cited by 34 (4 self)
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We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of atthemoney and outofthemoney options as the option maturity approaches zero. We show that these prices converge to zero at speeds which depend upon whether the sample path of the underlying asset price process is purely continuous, purely discontinuous, or a mixture of both. By applying the test to S&P 500 index options data, we conclude that the sample path behavior of this index contains both a continuous component and a jump component. In particular, we find that while the presence of the jump component varies strongly over time, the presence of the continuous component is constantly felt. We investigate the implications of the evidence for parametric model specifications.
Microeconomic Models for LongMemory in the Volatility of Financial Time Series
"... We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical longmemory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired ..."
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Cited by 27 (2 self)
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We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical longmemory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly, or indirectly by those of the other participants. These "field effects" generate "herding" behaviour which affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are I(0), the series of absolute and squared returns display strong dependence, while the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common longmemory properties in the volatility and covolatility of financial time series, revealed by Teyssière (1997, 1998a). These properties are investigated by using various model independent tests and estimators, i.e., semiparametric and nonparametric, introduced by Lo (1991), Kwiatkowski, Phillips, Schmidt and Shin (1992), Robinson (1995), Lobato and Robinson (1998), Giraitis, Kokoszka Leipus and Teyssière (2000, 2001). The relative performance of these tests and estimators for longmemory in a nonstandard data generating process is then assessed.
Change of structure in financial time series, long range dependence and the GARCH model
, 1999
"... Functionals of a twoparameter integrated periodogram have been used for a long time for detecting changes in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram having as limit a Gaussian field. In the ..."
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Cited by 25 (0 self)
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Functionals of a twoparameter integrated periodogram have been used for a long time for detecting changes in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram having as limit a Gaussian field. In the case of GARCH(p; q) processes a statistic closely related to the integrated periodogram can be used for the purpose of change detection in the model. We derive a central limit theorem for this statistic under the hypothesis of a GARCH(p; q) sequence with a finite 4th moment. When applied to reallife time series our method gives clear evidence of the fast pace of change in the data. One of the straightforward conclusions of our study is the infeasibility of modeling long return series with one GARCH model. The parameters of the model must be updated and we propose a method to detect when the update is needed. Our study supports the hypothesis of global nonstationarity of the return time ser...
2007): “MIDAS regressions: Further results and new directions,” Econometric Reviews
"... We explore Mixed Data Sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. ..."
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Cited by 25 (4 self)
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We explore Mixed Data Sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not so recent literature on distributed lag models. We study various lag structures to parameterize parsimoniously the regressions and relate them to existing models. We also propose several new extensions of the MIDAS framework. The paper concludes with an empirical section where we provide further evidence and new results on the riskreturn tradeoff. We also report empirical evidence on microstructure noise and volatility forecasting. We thank two Referees and an Associate Editor, Alberto Plazzi, Pedro SantaClara as well as seminar