Zi-Yi Guo

Correspondence: Zi-Yi Guo, Zach.Guo@wellsfargo.com

Corporate Model Risk Management Group, Wells Fargo Bank, N.A

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Abstract

Traditional econometric modelling typically follows the idea that market returns follow a normal distribution. However, the concept of tail risk indicates that the distribution of returns is not normal, but skewed and has heavy tails. Thus, a heavy-tailed distribution, which accurately estimates the tail risk, would significantly improve quantitative risk management practice. In this paper, we compare four widely used heavy-tailed distributions using the S&P 500 daily returns. Our results indicate that the Skewed t distribution in Hansen (1994) has the superior empirical performance compared with the Student’s t distribution, the normal reciprocal inverse Gaussian distribution and the generalized hyperbolic distribution. We further showed the Skewed t distribution could generate the VaR estimates closest to the nonparametric historical VaR estimates compared with other heavy-tailed distributions.

Keywords:

  Tail risk; Value at Risk; Goodness of fit.

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