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Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

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Noise Dressing of Financial Correlation Matrices

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price…
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Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes

Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range…
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Statistical properties of stock order books: empirical results and models

Abstract We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most…
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How Markets Slowly Digest Changes in Supply and Demand

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how…
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HERD BEHAVIOR AND AGGREGATE FLUCTUATIONS IN FINANCIAL MARKETS

We present a simple model of a stock market where a random communication structure between agents generically gives rise to heavy tails in the distribution of stock price variations in the form of an…
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Theory Of Financial Risk And Derivative Pricing

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the…
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Weak ergodicity breaking and aging in disordered systems

We present a phenomenological model for the dynamics of disordered (complex) systems. We postulate that the lifetimes of the many metastable states are distributed according to a broad, power law…
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Cleaning large correlation matrices: tools from random matrix theory

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Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management

Foreword Preface 1. Probability theory: basic notions 2. Maximum and addition of random variables 3. Continuous time limit, Ito calculus and path integrals 4. Analysis of empirical data 5. Financial…
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