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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.
The Asymptotic Efficiency Of Simulation Estimators
 Operations Research
, 1992
"... A decisiontheoretic framework is proposed for evaluating the efficiency of simulation estimators. The framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate. The cost of obtaining the estimate and the estimate itself are represented as realizations ..."
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Cited by 43 (14 self)
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A decisiontheoretic framework is proposed for evaluating the efficiency of simulation estimators. The framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate. The cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes. In this context, the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk (the overall expected cost). This framework is appealing philosophically, but it is often difficult to apply in practice (e.g., to compare the efficiency of two different estimators) because only rarely can the efficiency associated with a given computational budget be calculated. However, a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases. A limit theorem established for this model supports and extends a fairly well known e...
Institutional investors and stock market volatility
, 2006
"... We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid markets. Such trades generate significant spikes in returns and volume, even in the absence of important news about fundamentals. We derive ..."
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Cited by 26 (5 self)
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We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid markets. Such trades generate significant spikes in returns and volume, even in the absence of important news about fundamentals. We derive the optimal trading behavior of these investors, which allows us to provide a unified explanation for apparently disconnected empirical regularities in returns, trading volume and investor size. I.
A Multifractal Model of Asset Returns
, 1997
"... This paper presents the multifractal model of asset returns (“MMAR”), based upon ..."
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Cited by 23 (2 self)
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This paper presents the multifractal model of asset returns (“MMAR”), based upon
Optimal stopping and perpetual options for Lévy processes
, 2000
"... Solution to the optimal stopping problem for a L'evy process and reward functions (e x \Gamma K) + and (K \Gamma e x ) + , discounted at a constant rate is given in terms of the distribution of the overall supremum and infimum of the process killed at this rate. Closed forms of this solution ..."
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Cited by 22 (2 self)
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Solution to the optimal stopping problem for a L'evy process and reward functions (e x \Gamma K) + and (K \Gamma e x ) + , discounted at a constant rate is given in terms of the distribution of the overall supremum and infimum of the process killed at this rate. Closed forms of this solutions are obtained under the condition of positive jumps mixedexponentially distributed. Results are interpreted as admissible pricing of perpetual American call and put options on a stock driven by a L'evy process, and a BlackScholes type formula is obtained. Keywords and Phrases: Optimal stopping, L'evy process, mixtures of exponential distributions, American options, Derivative pricing. JEL Classification Number: G12 Mathematics Subject Classification (1991): 60G40, 60J30, 90A09. 1 Introduction and general results 1.1 L'evy processes Let X = fX t g t0 be a real valued stochastic process defined on a stochastic basis(\Omega ; F ; F = (F t ) t0 ; P ) that satisfy the usual conditions. A...
EFFICIENT MARKETS HYPOTHESIS
"... The efficient markets hypothesis (EMH) maintains that market prices fully reflect all available information. Developed independently by Paul A. Samuelson and Eugene F. Fama in the 1960s, this idea has been applied extensively to theoretical models and empirical studies of financial securities prices ..."
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Cited by 11 (0 self)
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The efficient markets hypothesis (EMH) maintains that market prices fully reflect all available information. Developed independently by Paul A. Samuelson and Eugene F. Fama in the 1960s, this idea has been applied extensively to theoretical models and empirical studies of financial securities prices, generating considerable controversy as well as fundamental insights into the pricediscovery process. The most enduring critique comes from psychologists and behavioural economists who argue that the EMH is based on counterfactual assumptions regarding human behaviour, that is, rationality. Recent advances in evolutionary psychology and the cognitive neurosciences may be able to reconcile the EMH with behavioural anomalies.
The Problem Of Optimal Asset Allocation With Stable Distributed Returns
 Stochastic Processes and Functional Analysis, Dekker Series of Lecture Notes in Pure and Applied Mathematics
, 2004
"... This paper discusses two optimal allocation problems. We consider different hypotheses of portfolio selection with stable distributed returns for each of them. In particular, we study the optimal allocation between a riskless return and risky stable distributed returns. Furthermore, we examine and c ..."
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Cited by 7 (4 self)
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This paper discusses two optimal allocation problems. We consider different hypotheses of portfolio selection with stable distributed returns for each of them. In particular, we study the optimal allocation between a riskless return and risky stable distributed returns. Furthermore, we examine and compare the optimal allocation obtained with the Gaussian and the stable nonGaussian distributional assumption for the risky return. KEY WORDS: optimal allocation, stochastic dominance, risk aversion, measure of risk, a stable distribution, domain of attraction, subGaussian stable distributed, fund separation, normal distribution, mean variance analysis, safetyfirst analysis. 2 1. INTRODUCTION This paper serves a twofold objective: to compare the normal with the stable nonGaussian distributional assumption when the optimal portfolio is to be chosen and to propose stable models for the optimal portfolio selection according to the utility theory under uncertainty. It is wellknown that asset returns are not normally distributed, but many of the concepts in theoretical and empirical finance developed over the past decades rest upon the assumption that asset returns follow a normal distribution. The fundamental work of Mandelbrot (1963ab, 1967ab) and Fama (1963,1965ab) has sparked considerable interest in studying the empirical distribution of financial assets. The excess kurtosis found in Mandelbrot's and Fama's investigations led them to reject the normal assumption and to propose the stable Paretian distribution as a statistical model for asset returns. The Fama and Mandelbrot's conjecture was supported by numerous empirical investigations in the subsequent years, (see Mittnik, Rachev and Paolella (1997) and Rachev and Mittnik (2000)). The practical and theoretical app...
Does Hollywood Make Too Many Rrated Movies? Risk, Stochastic Dominance, and the Illusion of Expectation
"... This paper estimates the probability distributions of budgets, revenues, returns and profits to G, PG, PG13, and Rrated movies. The distributions are nonGaussian and show a selfsimilar stable Paretian form with nonfinite variance and nonstationary mean. We stochastically rank these distr ..."
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Cited by 7 (1 self)
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This paper estimates the probability distributions of budgets, revenues, returns and profits to G, PG, PG13, and Rrated movies. The distributions are nonGaussian and show a selfsimilar stable Paretian form with nonfinite variance and nonstationary mean. We stochastically rank these distributions to investigate film critic Michael Medved's argument that Hollywood overproduces Rrated movies. The evidence shows that the industry's critics and its shareholders can agree that Hollywood does make too many trashy movies. The profit distributions have aysmmetric tails which means that Hollywood could trim its "downside" risk while increasing its "upside" possibilities by shifting production dollars out of Rrated movies into G, PG, and even PG13 movies. Stars who are willing to appear in edgy, counterculture Rrated movies for their prestige value may induce an "illusion of expectation " leading a studio to "greenlight" movies that have biased expectations.
Geometric Lévy Process Pricing Model
 Proceedings of Steklov Mathematical Institute
, 2002
"... We consider models for stock prices which relates to random processes with independent homogeneous increments (Levy processes). These models are arbitrage free but correspond to the incomplete financial market. There are many different approaches for pricing of financial derivatives. We consider her ..."
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Cited by 4 (3 self)
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We consider models for stock prices which relates to random processes with independent homogeneous increments (Levy processes). These models are arbitrage free but correspond to the incomplete financial market. There are many different approaches for pricing of financial derivatives. We consider here mainly the approach which is based on minimal relative entropy. This method is related to an utility function of exponential type and the Esscher transformation of probabilistic measures. 1
THE INEFFICIENT MARKETS HYPOTHESIS: WHY FINANCIAL MARKETS DO NOT WORK WELL IN THE REAL WORLD
"... Abstract. Existing literature continues to be unable to offer a convincing explanation for the volatility of the stochastic discount factor in real world data. Our work provides such an explanation. We do not rely on frictions, market incompleteness or transactions costs of any kind. Instead, we mod ..."
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Cited by 3 (0 self)
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Abstract. Existing literature continues to be unable to offer a convincing explanation for the volatility of the stochastic discount factor in real world data. Our work provides such an explanation. We do not rely on frictions, market incompleteness or transactions costs of any kind. Instead, we modify a simple stochastic representative agent model by allowing for birth and death and by allowing for heterogeneity in agents ’ discount factors. We show that these two minor and realistic changes to the timeless ArrowDebreu paradigm are sufficient to invalidate the implication that competitive financial markets efficiently allocate risk. Our work demonstrates that financial markets, by their very nature, cannot be Pareto efficient, except by chance. Although individuals in our model are rational; markets are not. I.