PT Unknown
AU Schmitt, T
TI Non-stationarity as a central aspect of financial markets
PD 12
PY 2014
LA en
AB We leverage methods from statistical physics to study problems in economics, particularly financial markets. While there are some examples in history where physicists contributed to problems in economics, both sciences developed independently.</br>
The interdisciplinary field of econophysics has been formed during
the last twenty years to facilitate the transfer of methods.
We start by investigating the influence of the non-stationarity in financial time series on portfolio optimization and assess different methods designed to suppress the negative effects on the covariance estimation. The study compares different models to estimate the covariance matrix and how combinations of refinements can improve on them. The effectiveness of the refinements depends on the covariance estimators and they are essential to receive good results for portfolio optimization.</br>
The temporal dependencies inherent in financial time series are investigated with a recently introduced quantile-based correlation function. The results provide a much broader overview of the time series’ features compared to the classic method of studying the autocorrelation of the absolute or squared returns. In addition, we study how well different common stochastic processes capture the features of empirical time series and find striking differences.
To model the influence of the non-stationarity, we use an ensemble approach to construct a multivariate correlation-averaged normal distribution, which addresses the non-stationarity of the covariance matrix. We carry out an extensive empirical study to validate the approach.</br>
The correlation-averaged normal distribution is then used as a realistic distribution for the asset values in the Merton model. We calculate the average loss distribution which takes the non-stationarity into account. This approach yields a quantitative understanding of why the benefits of diversification are limited. As practitioner-oriented risk measures we investigate the Value at
Risk and Expected Tail Loss for credit portfolios.
ER