Results 1  10
of
42
WideArea Traffic: The Failure of Poisson Modeling
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1995
"... Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 widearea traces, investigating a number of widearea TCP arrival processes (session and con ..."
Abstract

Cited by 1405 (21 self)
 Add to MetaCart
Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 widearea traces, investigating a number of widearea TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that userinitiated TCP session arrivals, such as remotelogin and filetransfer, are wellmodeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into “connection bursts,” the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible selfsimilarity of widearea traffic.
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 ..."
Abstract

Cited by 89 (12 self)
 Add to MetaCart
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.
Quantitative stability in stochastic programming: The method of probability metrics
, 2000
"... Quantitative stability of optimal values and solution sets to stochastic programming problems is studied when the underlying probability distribution varies in some metric space of probability measures. We give conditions that imply that a stochastic program behaves stable with respect to a minim ..."
Abstract

Cited by 27 (12 self)
 Add to MetaCart
Quantitative stability of optimal values and solution sets to stochastic programming problems is studied when the underlying probability distribution varies in some metric space of probability measures. We give conditions that imply that a stochastic program behaves stable with respect to a minimal information (m.i.) probability metric that is naturally associated with the data of the program. Canonical metrics bounding the m.i. metric are derived for specic models, namely for linear twostage, mixedinteger twostage and chance constrained models. The corresponding quantitative stability results as well as some consequences for asymptotic properties of empirical approximations extend earlier results in this direction. In particular, rates of convergence in probability are derived under metric entropy conditions. Finally, we study stability properties of stable investment portfolios having minimal risk with respect to the spectral measure and stability index of the underly...
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 ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
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...
Pure Jump Lévy Processes for Asset Price Modelling
, 2004
"... The goal of the paper is to show that some types of Lvy processes such as the hyperbolic motion and the CGMY are particularly suitable for asset price modelling and option pricing. We wish to review some fundamental mathematic properties of Lvy distributions, such as the one of infinite divisibility ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
The goal of the paper is to show that some types of Lvy processes such as the hyperbolic motion and the CGMY are particularly suitable for asset price modelling and option pricing. We wish to review some fundamental mathematic properties of Lvy distributions, such as the one of infinite divisibility, and how they translate observed features of asset price returns. We explain how these processes are related to Brownian motion, the central process in finance, through stochastic time changes which can in turn be interpreted as a measure of the economic activity. Lastly, we focus on two particular classes of pure jump Lvy processes, the generalized hyperbolic model and the CGMY models, and report on the goodness of fit obtained both on stock prices and option prices.
Traffic selfsimilarity
 In IEEE International Conference on Telecommunications (ICT) Tutorial
, 2001
"... The unifying concept underlying fractals, chaos and power laws is selfsimilarity. Selfsimilarity, or invariance against changes in scale or size, is an attribute of many laws of nature and innumerable phenomena in the world around us. Selfsimilarity is, in fact, one of the decisive symmetries tha ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
The unifying concept underlying fractals, chaos and power laws is selfsimilarity. Selfsimilarity, or invariance against changes in scale or size, is an attribute of many laws of nature and innumerable phenomena in the world around us. Selfsimilarity is, in fact, one of the decisive symmetries that shapes our universe and our efforts to comprehend it.
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 ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
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.
High volatility, thick tails and extreme value theory in valueatrisk estimation
 Insurance: Mathematics and Economics
, 2003
"... In this paper, the performance of the extreme value theory in ValueatRisk calculations is compared to the performances of other wellknown modeling techniques, such as GARCH, variancecovariance method and historical simulation in a volatile stock market. The models studied can be classified into ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
In this paper, the performance of the extreme value theory in ValueatRisk calculations is compared to the performances of other wellknown modeling techniques, such as GARCH, variancecovariance method and historical simulation in a volatile stock market. The models studied can be classified into two groups. The first group consists of GARCH(1,1) and GARCH(1,1)t models which yield highly volatile quantile forecasts. The other group, consisting of historical simulation, variancecovariance approach, adaptive generalized pareto distribution (GPD) and nonadaptive GPD models leads to more stable quantile forecasts. The quantile forecasts of GARCH(1,1) models are excessively volatilite relative to the GPD quantile forecasts. This makes the GPD model to be a robust quantile forecasting tool which is practical to implement and regulate for VaR measurements. Key Words: ValueatRisk, financial risk management, extreme value theory.