Options markets offer an interesting example of the adaptation of a population to a complex environment, through trial and error and by 'natural' selection. Guided by the Black-Scholes theory but constrained by the fact that mispricing leads to arbitrage opportunities, options markets agree on...

We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered...

We show how one can actually take advantage of the strongly non-Gaussian nature of the fluctuations of financial assets to simplify the calculation of the Value-at-Risk of complex non linear portfolios. The resulting equations are not hard to solve numerically, and should allow fast VaR and...

Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for derivative markets. Classical theories, however, are...

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 fluctuations. The central result of the present study is the remarkable agreement between the...

We study a generic model for self-referential behaviour in financial markets, where agents attempt to use some (possibly fictitious) causal correlations between a certain quantitative information and the price itself. This correlation is estimated using the past history itself, and is used by a...

Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market...

The simplest field theory description of the multivariate statistics of forward rate variations over time and maturities, involves a quadratic action containing a gradient squared rigidity term. However, this choice leads to a spurious kink (infinite curvature) of the normalized correlation...

We study Sutton's `microcanonical' model for the internal organisation of firms, that leads to non trivial scaling properties for the statistics of growth rates. We show that the growth rates are asymptotically Gaussian in this model, at variance with empirical results. We also obtain the...

We propose a new `hedged' Monte-Carlo (HMC) method to price financial derivatives, which allows to determine simultaneously the optimal hedge. The inclusion of the optimal hedging strategy allows one to reduce the financial risk associated with option trading, and for the very same reason...