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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 149 (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 Supremum of a Negative Drift Random Walk with Dependent HeavyTailed Steps
, 1998
"... . Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady s ..."
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Cited by 39 (25 self)
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. Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady state distribution of the number of customers in the system or the value at risk. When the stationary process is heavytailed, the corresponding ruin probabilities are high and the stationary distributions are heavytailed as well. If the steps of the random walk are independent, then the exact asymptotic behavior of such probability tails was described by Embrechts and Veraverbeke (1982). We show that this asymptotic behavior may be different if the steps of the random walk are not independent, and the dependence affects the joint probability tails of the stationary process. Such type of dependence can be modeled, for example, by a linear process. 1. Introduction In various applied fields...
How System Performance is Affected by the Interplay of Averages in a Fluid Queue with Long Range Dependence Induced by Heavy Tails
 Ann. Appl. Probab
, 1999
"... . We consider a fluid queue with sessions arriving according to a Poisson process. A longtailed distribution of session lengths induces long range dependence in the system and causes its performance to deteriorate. The deterioration is due to occurrence of load regimes far from average ones. Nonet ..."
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Cited by 17 (9 self)
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. We consider a fluid queue with sessions arriving according to a Poisson process. A longtailed distribution of session lengths induces long range dependence in the system and causes its performance to deteriorate. The deterioration is due to occurrence of load regimes far from average ones. Nonetheless, the extent of this performance deterioration is shown to depend crucially on the average values of the system parameters. 1. Introduction We consider the following fluid queuing model. Sessions (ON periods) are initiated at a network server or multiplexer according to a Poisson process with rate ? 0. Each session is active for a random length of time with distribution F and a finite mean ; during this time it generates network traffic at unit rate. We assume that the lengths of different sessions are independent, and they are also independent of the Poisson arrival process. The service rate is r ? 0 units of traffic per unit time. If X(t) denotes the amount of work (measured in unit...
Multivariate Extremes at Work for Portfolio Risk
 Management,” Working Paper, Financial Econometrics Research
, 2001
"... This paper proposes a methodology to provide risk measures for portfolios during extreme events. The approach is based on splitting the multivariate extreme value distribution of the assets of the portfolio into two parts: the distributions of each asset and their dependence function. The estimation ..."
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Cited by 4 (0 self)
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This paper proposes a methodology to provide risk measures for portfolios during extreme events. The approach is based on splitting the multivariate extreme value distribution of the assets of the portfolio into two parts: the distributions of each asset and their dependence function. The estimation problem is also investigated. Then, stresstesting is applied for market indices portfolios and MonteCarlo based risk measures – ValueatRisk and Expected Shortfall – are provided.
Ruin Problem, Operational Risk And How Fast Stochastic Processes Mix
 C3 National Highway and Safety Administration, Strategic Plan
, 2001
"... The recent increasing interplay between actuarial and financial mathematics has led to a surge of risk theoretic modeling. Especially actuarial ruin models under fairly general conditions on the underlying risk process have become a focus of attention. Motivated by applications to the modeling of op ..."
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Cited by 3 (1 self)
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The recent increasing interplay between actuarial and financial mathematics has led to a surge of risk theoretic modeling. Especially actuarial ruin models under fairly general conditions on the underlying risk process have become a focus of attention. Motivated by applications to the modeling of operational risk losses in financial risk management, we investigate the stability of classical asymptotic ruin estimates when claims are heavy, and this under variability of the claim intensity process. Various examples are discussed. 1.
Tail Probabilities Of Subadditive Functionals Acting On Lévy Processes
"... . We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of L'evy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the ..."
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Cited by 1 (1 self)
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. We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of L'evy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our results apply to ruin probabilities, distributions of sojourn times over curves, last hitting times and other functionals. 1. Introduction Both in the theory and in applications of stochastic processes one is often interested in two types of questions: When does the process X = fX(t); t 0g lie above a certain deterministic function (curve) = f(t); t 0g, and given the process exceeds this curve, what are its values? For example, what can be said about the distribution of the biggest excess of the process over the curve and, if both the process and the function are measurable, what is the di...
Ruin Probability With Claims Modeled By A Stationary Ergodic Stable Process
, 1999
"... . For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin probabi ..."
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. For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin probability for a large variety of stationary ergodic stable processes. Our findings show that the order of magnitude of the ruin probability varies significantly from one model to another. In particular, ruin becomes much more likely when the claim sizes exhibit longrange dependence. The proofs exploit large deviation techniques for sums of dependent stable random variables and the series representation of a stable process as a function of a Poisson process. 1991 Mathematics Subject Classification. Primary 60E07, 60G10; Secondary 60K30. Key words and phrases. Stable process, stationary process, ruin probability, heavy tails, supremum, negative drift, risk. Research supported by NATO Collaborative...
Presented at the 9th Annual IFCI Risk Management Round Table Dynamic ValueatRisk with HeavyTailed Distributions: Portfolio Study
"... Abstract. Different Monte Carlo copulabased ValueatRisk (VaR) models are presented and numerical results on real portfolios are reported. The models feature two families of heavytailed univariate distributions: Studentt and Stable. A generalized autoregressive conditional heteroskedastic (GARCH ..."
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Abstract. Different Monte Carlo copulabased ValueatRisk (VaR) models are presented and numerical results on real portfolios are reported. The models feature two families of heavytailed univariate distributions: Studentt and Stable. A generalized autoregressive conditional heteroskedastic (GARCH) Studentt process is considered and implemented to enhance the static models. Comparisons with other commonlyused VaR models are included. It is numerically demonstrated that the GARCHStudentt models estimate rather accurately highquantile VaR measures and outperform the rest of the considered models. The views expressed in this article are solely the authors ’ opinions, and are not supported or shared by The Options Clearing Corporation. § To whom correspondence should be addressed (sivanov@theocc.com) Dynamic ValueatRisk with HeavyTailed Distributions: Portfolio Study 2
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quant.iop.org Empirical properties of asset returns: stylized facts and statistical issues