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Stochastic modelling of random variables
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The process of verifying how well a selected and calibrated model represents a certain empirically observed phenomenon is usually referred to as model validation. In areas where empirical phenomena are not directly observable, as in case of financial volatility, the problem of stochastic model validation remains perhaps one of the most elusive though practically relevant problems of the modern applied research. In particular, it is generally preferable to use some form of objective analysis to perform the model validation. In this study, the stochastic process that underlies dynamics of financial variables is examined using statistical hypothesis testing and simulation techniques. We discover an interesting empirical anomaly never noticed before. It will be demonstrated that the observed artefact could be expected if the specifics of financial markets were appropriately taken into account and the analytical instrument was used with proper discretion. The obtained knowledge will be applied in validation and improvement of a stochastic model that measures a financial risk exposure.
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