Results 1  10
of
34
The Distribution of Realized Exchange Rate Volatility
 Journal of the American Statistical Association
, 2001
"... Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately ..."
Abstract

Cited by 155 (18 self)
 Add to MetaCart
Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normalityinducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of longmemory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.
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 ..."
Abstract

Cited by 155 (2 self)
 Add to MetaCart
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.
On Estimating the Intensity of LongRange Dependence in Finite and Infinite Variance Time Series
, 1996
"... The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of longrange dependence in time series. It provides a detailed comparison of eight estimators for longrange dependence, using simulated FARIMA(p; d; q) time series with different finite and infinite var ..."
Abstract

Cited by 41 (3 self)
 Add to MetaCart
The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of longrange dependence in time series. It provides a detailed comparison of eight estimators for longrange dependence, using simulated FARIMA(p; d; q) time series with different finite and infinite variance innovations. FARIMA time series model both longrange dependence (through the parameter d) and shortrange dependence (through the parameters p and q). We evaluate the biases and standard deviations of several estimators of d and compare them for each type of series used. We consider Gaussian, exponential, lognormal, Pareto, symmetric and skewed stable innovations. Detailed tables and graphs have been included. We find that the estimators tend to perform less well when p and q are not zero, that is, when there is additional shortrange dependence structure. For most of the estimators, however, the use of infinite variance instead of finite variance innovations does not cause a great dec...
A Langevin approach to stock market fluctuations and crashes
 EUROPEAN PHYSICS JOURNAL B
, 1998
"... We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize the importance of feedback e#ects of price va ..."
Abstract

Cited by 31 (4 self)
 Add to MetaCart
We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize the importance of feedback e#ects of price variations onto themselves. Risk aversion, in particular, leads to an "updown" symmetry breaking term which is responsible for crashes, where "panic" is self reinforcing. It is also responsible for the sudden collapse of speculative bubbles. Interestingly, these crashes appear as rare, "activated" events, and have an exponentially small probability of occurence. The model leads to a specific "shape" of the falldown of the price during a crash, which we compare with the October 1987 data. The normal regime, where the stock price exhibits behavior similar to that of a random walk, however reveals non trivial correlations on different time scales, in particular on the time scale over which operators perceive a change of trend.
NonStationarities in Stock Returns
, 2001
"... Modeling financial returns on longer time intervals under the assumption of stationarity is, at least intuitively, given the pace of change in world's economy, a choice hard to defend. Relinquishing the global stationarity hypothesis, this paper conducts a data analysis focused on the size of the ..."
Abstract

Cited by 20 (1 self)
 Add to MetaCart
Modeling financial returns on longer time intervals under the assumption of stationarity is, at least intuitively, given the pace of change in world's economy, a choice hard to defend. Relinquishing the global stationarity hypothesis, this paper conducts a data analysis focused on the size of the returns, i.e. the absolute values of returns, under the assumptions that, at least locally, the S&P500 daily return series can be modeled by stationary processes. The challenging task when working under the assumption of local stationarity is to define the intervals on which stationary processes provide a good approximation. This task is accomplished by using a goodness of fit test based on the integrated periodogram (Picard ([21]), Kluppelberg and Mikosch ([15])). The conclusion of the paper is that almost all the dynamics of return time series seem to be concentrated in the shifts of the variance. More concretely, the S&P500 absolute returns, jr j can be modeled as jr j = h(t)exp(ffl t ); t = 0; 1; : : : where (ffl t ) is white noise, E ffl = 0, E ffl and h(t) a function of t which can be well approximated by a step function, yielding a model with piecewise constant variance.
Financial Markets as Adaptive Systems
, 1998
"... We show, by studying in detail the market prices of options on liquid markets, that the market has empirically corrected the simple, but inadequate BlackScholes formula to account for two important statistical features of asset fluctuations: "fat tails" and correlations in the scale of fluctuations ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
We show, by studying in detail the market prices of options on liquid markets, that the market has empirically corrected the simple, but inadequate BlackScholes formula to account for two important statistical features of asset fluctuations: "fat tails" and correlations in the scale of fluctuations. These aspects, although not included in the pricing models, are very precisely reflected in the price fixed by the market as a whole. Financial markets thus behave as rather efficient adaptive systems.
Refined inference on longmemory in realized volatility
, 2006
"... There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et. al. (2001), Martens et. al. (2004)). The present paper provides some analytical explanations for this evidence and shows ho ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et. al. (2001), Martens et. al. (2004)). The present paper provides some analytical explanations for this evidence and shows how recent results in Lieberman and Phillips (2004a, 2004b) can be used to refine statistical inference about d with little computational effort. In contrast to standard asymptotic normal theory now used in the literature which has an O ¡ n −1/2 ¢ error rate on error rejection probabilities, the asymptotic approximation used here has an error rate of o ¡ n −1/2 ¢. The new formula is independent of unknown parameters, is simple to calculate and highly userfriendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et. al. (2001) and Martens et. al. (2004) differ significantly from the lower boundary (d =0.5) of nonstationary long memory.
Elements for a theory of financial risks
 PHYSICA A
, 1999
"... Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditional theories based on Gaussian statistics), and their practical implementation. Here we ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditional theories based on Gaussian statistics), and their practical implementation. Here we describe three interrelated aspects of this program: we first give a brief survey of the peculiar statistical properties of the empirical price fluctuations. We then review how an option pricing theory consistent with these statistical features can be constructed, and compared with real market prices for options. We finally argue that a true ‘microscopic ’ theory of price fluctuations (rather than a statistical model) would be most valuable for risk assessment. A simple Langevinlike equation is proposed, as a possible step in this direction.