Extremes

Financial assets

In this example we will show the probability distribution of the fluctuation of exchange rate over a period of minutes, the rate variations can be considered as Gaussian approximation. The mean observation shows that for minutes, the variations are strongly non-gaussian.

Presentation of the probability density function at τ =8 minutes s for FX DM/$ index and comparison with empirical data [J.M Tcheou, M. Brachet et E. Taflin, 2000]InformationInformation[1]

This is very important for risk assessment: the non-Gaussian nature of the probability distribution is so pronounced that using a Gaussian approximation would lead to significant errors.

  1. Brachet, M. E., Taflin, E., & Tcheou, J. M. (2000). Scaling transformation and probability distributions for financial time series. Chaos, Solitons & Fractals, 11(14), 2343-2348.

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