Density forecasting in financial risk modelling
As a result of an increasingly stringent regulation aimed at monitoring financial risk exposures, nowadays the risk measurement systems play a crucial role in all banks. In this thesis we tackle a variety of problems, related to density forecasting, which are fundamental to market risk managers. The computation of risk measures (e.g. Value-at-Risk) for any portfolio of financial assets requires the generation of density forecasts for the driving risk factors. Appropriate testing procedures must then be identified for an accurate appraisal of these forecasts. We start our research by assessing whether option-implied densities, which constitute the most obvious forecasts of the distribution of the underlying asset at expiry, do actually represent unbiased forecasts. We first extract densities from options on currency and equity index futures, by means of both traditional and original specifications. We then appraise them, via rigorous density forecast evaluation tools, and we find evidence of the presence of biases. In the second part of the thesis, we focus on modelling the dynamics of the volatility curve, in order to measure the vega risk exposure for various delta-hedged option portfolios. We propose to use a linear Kalman filter approach, which gives more precise forecasts of the vega risk exposure than alternative, well-established models. In the third part, we derive a continuous time model for the dynamics of equity index returns from a data set of 5-minute returns. A model inferred from high-frequency typical of risk measures calculations. The last part of our work deals with evaluating density forecasts of the joint distribution of the risk factors. We find that, given certain specifications for the multivariate density forecast, a goodness-of-fit procedure based on the Empirical Characteristic Function displays good statistical properties in detecting misspecifications of different nature in the forecasts.