Handbook of Heavy Tailed Distributions in Finance

7 Applications

In this section we present an example of fitting bivariate financial data sets with stable models. We Iit a bivariate stable and a bivariate operator stable models to two data sets. Our data consists of 1162 daily DAX30 Index (DAX), FTSE100 Index (UKX), and S&P500 Index (SPX) prices for the period from 1/1/95 to 11/3/99. The raw indexes are first transformed into log-returns by taking natural logarithms of the quotients of their consecutive values. We analyze log-returns (1161 observations) ${\text{X}}_t=\ln (Y_t/Y_{t-1})$, where the Y_t's are the raw daily index prices. The goal is to Iit reasonable models to the bivariate vectors (DAX, UKX) and (UKX, ...