Estimating financial risk using piecewise Gaussian processes

Abstract

We present a computational method for measuring financial risk by estimating the Value at Risk and Expected Shortfall from financial series. We have made two assumptions: First, that the predictive distributions of the values of an asset are conditioned by information on the way in which the variable evolves from similar conditions, and secondly, that the underlying random processes can be described using piecewise Gaussian processes. The performance of the method was evaluated by using it to estimate VaR and ES for a daily data series taken from the S&P500 index and applying a backtesting procedure recommended by the Basel Committee on Banking Supervision. The results indicated a satisfactory performance.