Calibrating and Simulating Copula Functions in Financial Applications - Di Clemente, Annalisa; Romano, Claudio (Frontiers in Applied Mathematics and Statistics, 2021)
Copula functions can be utilized in financial applications to determine the dependence structure of the financial asset returns in the portfolio. Empirical evidence has proved the inadequacy of the multi-normal distribution, traditionally adopted to model the financial asset returns distribution. Copula functions can be employed in a flexible way for building efficient algorithms and to simulate a more adequate distribution of the financial assets. This paper aims to describe some simple statistical procedures currently employed to calibrate the copula functions to the financial market data. Furthermore, we present some useful methods for choosing which copula function better fits the real financial data. Also, some algorithms to simulate random variates from certain types of copula functions are illustrated. Finally, for example purposes, the procedures previously described are applied to two important Italian equities. In particular, we show how to generate efficient Monte Carlo scenarios of equity log-returns in the bivariate case using different types of copula functions.