Modelli basati sulla tecnica FGD multivariata per la stima di superfici di volatilità implicita e la previsione della curva dei tassi

The project is on the development of a set of multivariate methods for estimating and forecasting the dynamics of implied volatility surfaces and term structure curves. The focus of this research project is on multivariate statistical procedures which are computationally feasible also for very high-dimensional set-ups. Specifically, in our approach no variance reduction strategy is needed (such as for example principal component analysis), so that the complex structure of changing risk and volatilities can be accurately estimated when optimizing the risk management of dynamic portfolios.
In a CNNR subproject at USI (project number 6) we apply these techniques to the multivariate risk management of dynamic equity and derivatives portfolios. In this project, our aim is to extend that work to the research area of implied volatility surfaces and yield curves forecasting. Within this general setting we plan to consider the two following issues.
1. The most studies about the dynamic properties of implied volatility surfaces start with a cross-sectional analysis of the relevant surface. Thereby, a series of (smiles or term structures) curves is obtained to which a principal component analysis (PCA) is applied. At this stage, a complete study of the joint dynamics of all implied volatilities -looking simultaneously at all available maturities and moneyness parameters- can be performed without resorting to variance reduction techniques.
2. The term structure of interest rates has been often estimated and forecasted by imposing a particular parametric factor model or some low dimensional semi-parametric structure. This allows to overcome the curse of dimensionality problem and to reduce the complexity of the estimation procedure. At this stage, a multivariate semi-parametric approach for forecasting the whole term structure dynamics can be applied.
The project is on some specific aspects related to 1. and 2. A first part focuses on procedures for financial function estimation in very large dimensions (see for example Audrino and Bühlmann, 2003, Journal of Computational Finance, for an application to a multivariate conditional volatility matrix estimation problem). A second part is related to the calibration of such procedures to obtain accurate forecasts and to improve the computation of risk measures and fair prices for large dynamic bond and equity portfolios.