Robust risk management. Accounting for nonstationarity and heavy tails
- Chen, Ying
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62G05 62P20
- exponential smoothing, spatial aggregation, heavy-tailed distribution
In the ideal Black-Scholes world, financial time series are assumed 1) stationary (time homogeneous) or can be modelled globally by a stationary process and 2) having conditionally normal distribution given the past. These two assumptions have been widely-used in many methods such as the RiskMetrics, one risk management method considered as industry standard. However these assumptions are unrealistic. The primary aim of the paper is to account for nonstationarity and heavy tails in time series by presenting a local exponential smoothing approach, by which the smoothing parameter is adaptively selected at every time point and the heavy-tailedness of the process is considered. A complete theory addresses both issues. In our study, we demonstrate the implementation of the proposed method in volatility estimation and risk management given simulated and real data. Numerical results show the proposed method delivers accurate and sensitive estimates.