We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for Gaussian price increments, the correlations are...

We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments distribution and the decay of the volatility correlations are...

It is commonly believed that the correlations between stock returns increase in high volatility periods. We investigate how much of these correlations can be explained using conditional averages within a simple one-factor description. Using surrogate data with the true market return as 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...

We present compelling empirical evidence for a new interpretation of the Forward Rate Curve (FRC) term structure. We find that the average FRC follows a square-root law, with a prefactor related to the spot volatility, suggesting a Value-at-Risk like pricing. We find a striking correlation...

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...

In this paper we study empirically the Forward Rate Curve (FRC) of 5 different currencies. We confirm and extend the findings of a previous investigation of the U.S. FRC. In particular, the average FRC follows a square-root law, with a prefactor related to the spot volatility, suggesting a...

We present a exactly soluble model for financial time series that mimics the long range volatility correlations known to be present in financial data. Although our model is 'monofractal' by construction, it shows apparent multiscaling as a result of a slow crossover phenomenon on finite time...

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...

This paper contains a statistical description of the whole U.S. forward rate curve (FRC), based on data from the period 1990-1996. We find that the average deviation of the FRC from the spot rate grows as the square-root of the maturity, with a proportionality constant which is comparable to the...