Seminario di Fabio Gobbi a Bologna - Random - Mailing list

27 Jan 2014


      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.