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.