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A0838
Title: Empirical comparison of several skew-$t$ copulas Authors:  Toshinao Yoshiba - Bank of Japan (Japan) [presenting]
Abstract: In financial portfolio risk management, Student-$t$ copula is frequently used to capture the tail dependence of risk factors. Azzalini-Capitanio (AC) and Generalized Hyperbolic (GH) skew-$t$ copulas are considered to incorporate asymmetric tail dependence of risk factors. Two problems are indicated in estimating the parameters of the skew-$t$ copulas by maximizing the log-likelihood for pseudo observations. The first problem is the calculation speed of the log-likelihood function including univariate skew-$t$ quantile functions. The second problem is the positive semi-definiteness of the correlation matrix in the parameters. Having solved the two problems, the estimated parameters of the AC skew-$t$, GH skew-$t$, Student-$t$, skew-Normal, Normal copulas are compared for the daily returns of three major stock indices: the Nikkei225, S$\&$P500, and DAX. The asymmetric tail dependence is examined both for the unfiltered returns and for the filtered returns by GARCH and EGARCH models for the observation period of recent five-year and ten-year data. It shows that AC skew-$t$ copula with the same skewness is selected by AIC for both unfiltered and filtered returns. Regarding ten-year data, the AC skew-$t$ copula is selected even by BIC for both unfiltered and filtered returns.