Markov properties of high frequency exchange rate data

We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) p(x) on the delay time tau can be described by a Fokker-Planck equation, a gerneralized diffusion equation for p(x,tau). This equation is completely determined by two coefficients D_{1}(x,tau) and D_{2}(x,tau) (drift- and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker-Planck equation describe the empirical pdfs correctly, including the pronounced tails.Comment: 29 pages, 19 eps figures, misprints corrected, under consideration for publication in Physica

Microstructure Effects on Daily Return Volatility in Financial Markets

We simulate a series of daily returns from intraday price movements initiated by microstructure elements. Significant evidence is found that daily returns and daily return volatility exhibit first order autocorrelation, but trading volume and daily return volatility are not correlated, while intraday volatility is. We also consider GARCH effects in daily return series and show that estimates using daily returns are biased from the influence of the level of prices. Using daily price changes instead, we find evidence of a significant GARCH component. These results suggest that microstructure elements have a considerable influence on the return generating process.Comment: 15 pages, as presented at the Complexity Workshop in Aix-en-Provenc

Effects of Acute Acid Loading on the Risk of Calcium Phosphate and Calcium Oxalate Crystallization in Urine

The aim of this study was to examine the risk of calcium phosphate and calcium oxalate crystallization during acute acid loading under controlled conditions. The effects of acute acid loading on rates of renal excretion of calcium, magnesium, phosphate, citrate, oxalate and urine pH were studied in healthy subjects. The risk of calcium phosphate and calcium oxalate crystallization were evaluated by estimates of the ion activity products of calcium phosphate [AP(CaP)-index] and calcium oxalate [AP(CaOx)-index] according to Tiselius. In addition, the risk of brushite [AP(Bru)-index] crystallization was estimated. An acute acid load administered as ammonium chloride (NH4Cl) produced increased urinary excretion of calcium, phosphate and oxalate, decreased urinary excretion of citrate, and a decrease in urine pH. Consequently, calcium-citrate-ratio in urine increased markedly in response to acid loading. AP(CaP)-index decreased markedly due to a fall in urine pH. AP(Bru)-index decreased slightly and remained low throughout the study. AP(CaOx)-index increased significantly, and acid loading is suggested as a risk factor for calcium oxalate stone formation

A quantitative model of trading and price formation in financial markets

We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.Comment: 5 pages, 4 figure

Beta cell function after weight loss: a clinical trial comparing gastric bypass surgery and intensive lifestyle intervention

The effects of various weight loss strategies on pancreatic beta cell function remain unclear. We aimed to compare the effect of intensive lifestyle intervention (ILI) and Roux-en-Y gastric bypass surgery (RYGB) on beta cell function. Design One year controlled clinical trial (ClinicalTrials.gov identifier NCT00273104). One hundred and nineteen morbidly obese participants without known diabetes from the MOBIL study (mean (s.d.) age 43.6 (10.8) years, body mass index (BMI) 45.5 (5.6) kg/m2, 84 women) were allocated to RYGB (n=64) or ILI (n=55). The patients underwent repeated oral glucose tolerance tests (OGTTs) and were categorised as having either normal (NGT) or abnormal glucose tolerance (AGT). Twenty-nine normal-weight subjects with NGT (age 42.6 (8.7) years, BMI 22.6 (1.5) kg/m2, 19 women) served as controls. OGTT-based indices of beta cell function were calculated. One year weight reduction was 30 % (8) after RYGB and 9 % (10) after ILI (P<0.001). Disposition index (DI) increased in all treatment groups (all P<0.05), although more in the surgery groups (both P<0.001). Stimulated proinsulin-to-insulin (PI/I) ratio decreased in both surgery groups (both P<0.001), but to a greater extent in the surgery group with AGT at baseline (P<0.001). Post surgery, patients with NGT at baseline had higher DI and lower stimulated PI/I ratio than controls (both P<0.027). Gastric bypass surgery improved beta cell function to a significantly greater extent than ILI. Supra-physiological insulin secretion and proinsulin processing may indicate excessive beta cell function after gastric bypass surgery

Financial Market Efficiency Tests

This paper provides a selective survey of the voluminous literature on tests for market efficiency. The ideas discussed include standard autocorrelation tests, multi-period regression tests and volatility tests. The formulation and estimation of models for time-varying volatility are also considered. Dependence in second-order moments plays an important role in implementing and understanding tests for market efficiency. All of the reported test statistics and model estimates are calculated with monthly data on value-weighted NYSE stock prices and dividends. The distributions of the test statistics under various alternatives, including fads and bubbles, are illustrated through the use of Monte Carlo methods. In addition to the standard constant discount rate present value model, we postulate and simulate a new fundamental price relationship that accounts for the time-varying uncertainty in the monthly dividend growth rates. Allowing the discount rate to be a function of the time-varying uncertainty in the dividend process results in a simulated fundamental price series that is broadly consistent with most of the sample statistics of the actual data.

Multifractal model of asset returns with leverage effect

Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the Lux model and refine the underlying phenomenological picture. We also give a procedure of fitting all parameters to empirical data. We present a new approach to account for the effective length of power-law memory in volatility. The second part of the paper deals with the consequences of asymmetry in returns. We incorporate two related stylized facts, skewness and leverage autocorrelations into the model. Then from Monte Carlo measurements we show, that this asymmetry significantly increases the mean squared error of volatility forecasts. Based on a filtering method we give evidence on similar behavior in empirical data.Comment: 23 pages, 8 figures, updated some figures and references, fixed two typos, accepted to Physica

Elements for a Theory of Financial Risks

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 traditionnal 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 Langevin-like equation is proposed, as a possible step in this direction.Comment: 22 pages, to appear in `Order, Chance and Risk', Les Houches (March 1998), to be published by Springer/EDP Science

On a generalised model for time-dependent variance with long-term memory

The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.Comment: 6 pages, 4 figure