Romano_Copula_Paper

Romano_Copula_Paper - CALIBRATING AND SIMULATING COPULA...

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CALIBRATING AND SIMULATING COPULA FUNCTIONS: AN APPLICATION TO THE ITALIAN STOCK MARKET Claudio Romano 1 Abstract Copula functions are always more used in financial applications to determine the dependence structure of the asset returns in a portfolio. Empirical evidence has proved the inadequacy of the multinormal distribution, commonly adopted to model the asset return distribution. Copulas are flexible instruments used to build efficient algorithms for a better simulation of this distribution. The aim of this paper is describing the statistical procedures used to calibrate a copula function to real market data. Then, some methods used to choose which copula better fit data are presented. Finally a number of algorithms to simulate random variate from certain types of copula are illustrated. The procedures described are applied to a portfolio of Italian equities. We show how to generate efficient Monte Carlo scenarios of equity log-returns in the bivariate case using different copulas. Keywords: Copula Function, Dependence Structure, Multivariate Distribution Function. 1 Corresponding author: Claudio Romano, Risk Management Function, Capitalia, Viale U. Tupini, 180, 00144 – Rome, Italy. E-mail: [email protected] . The author is grateful to Prof. G. Szegö for his valuable comments and suggestions that helped improve the article substantially.
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2 CALIBRATING AND SIMULATING COPULA FUNCTIONS: AN APPLICATION TO THE ITALIAN STOCK MARKET Claudio Romano Introduction Copula functions are used in financial application since 1999 2 . Empirical evidence has proved that the multinormal distribution is inadequate to model portfolio asset return distribution under two points of view: 1) The empirical marginal distributions are skewed and fat tailed; 2) it does not consider the possibility of extreme joint co-movement of asset returns 3 . In other words, the dependence structure is different from the Gaussian one. Copula functions are a useful tool to implement efficient algorithms to simulate asset return distributions in a more realistic way. In fact, they allow to model the dependence structure indipendently from the marginal distributions. In this way, we may construct a multivariate distribution with different margins and the dependence structure given from the copula function. Therefore, a crucial step is the selection and the calibration of the copula function from real data. In this paper a collection of methods for calibrating, selecting and simulating copula functions are presented. Our aim is to collect in this article the principal contributions to the argument provided by the international literature cited in the references. Most of the method presented are applied to an empirical data set of the log- returns of two Italian equities. When it is possible, we show as the copula approach performs better than the multinormal distribution in modelling real data.
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Romano_Copula_Paper - CALIBRATING AND SIMULATING COPULA...

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