Il giorno Giovedì 30 Gennaio 2014, alle ore 14:30 presso la sede di Prometeia (sala grande, primo piano) via G.Marconi 43, Bologna
si terrà il
Seminario del Dott. Fabio Gobbi Dipartimento di Scienze Statistiche, Università di Bologna
Titolo: C-CONVOLUTION AND ITS APPLICATION TO FINANCE
Abstract In financial applications is interesting to determine the distribution function of the sum of two random variables X and Y in the case where they are dependent. We address the problem using the convolution operator which recovers the distribution of X+Y when a copula function C describes the dependence structure and the marginal distributions of the two r.vs. are given. Nevertheless, almost all the financial data are generated by stochastic processes. Our C-convolution approach allows to build dependent increments processes since setting X = X(t-1) − and Y = DX, their sum is X_t . In this framework we model the dependence structure between the level of the process and its next increment. From an empirical point of view, financial data are time series and the econometric analysis is provided by the concept of conditional copula introduced by Patton (2006) which allows us to define the conditional 𝐶-convolution as a data generating process. We estimate such a model by a three-stage maximum likelihood method and we provide some asymptotic results of this estimator. An immediate financial application of such a method is given by a copula-based model to recover the distribution of actively managed funds. The analysis is based on a general representation of the Henriksson Merton (1981) model, in which the forecasting ability of the asset manager is modeled with a copula function (linking the forecasts of the asset manager and actual market movements). This is a convolution-based copula yielding at the same time the marginal distribution of the return on the managed fund and the dependence structure between the managed fund and the market. The model is very well suited to estimate and simulate the conditional distribution of managed funds.