We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as Conditional Value-at-Risk). The only ingredient required by...

We present a neural-network valuation of financial derivatives in the case of fat-tailed underlying asset returns. A two-layer perceptron is trained on simulated prices taking into account the well-known effect of volatility smile. The prices of the underlier are generated using fractional...

At present, there is an explosion of practical interest in the pricing of interest rate (IR) derivatives. Textbook pricing methods do not take into account the leptokurticity of the underlying IR process. In this paper, such a leptokurtic behaviour is illustrated using LIBOR data, and a possible...

In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock prices, traded at NYSE, in October 1999. These properties...

In financial time series there are periods in which the value increases or decreases monotonically. We call those periods elemental trends and study the probability distribution of their duration for the indices DJIA, NASDAQ and IPC. It is found that the trend duration distribution often differs...

We present an experimental and simulated model of a multi-agent stock market driven by a double auction order matching mechanism. Studying the effect of cumulative information on the performance of traders, we find a non monotonic relationship of net returns of traders as a function of...

We propose a simple stochastic exchange game mimicking taxation and redistribution. There are g agents and n coins; taxation is modeled by randomly extracting some coins; then, these coins are redistributed to agents following Polya's scheme. The individual wealth equilibrium distribution for...