Estimating value at risk and expected shortfall: a kalman filter approach

Van Der Lecq, Maximilian

Estimating value at risk and expected shortfall: a kalman filter approach

Thesis / Dissertation

2024

Publisher

University of Cape Town

Department

School of Economics

Faculty

Faculty of Commerce

Abstract

Calculating Value-at-Risk (VaR) to estimate the maximum loss a portfolio may incur at a given confidence level and over a specified time has undergone several adaptations, iterations, and additions since its inception in 1994. In 2013, the Basel Committee on Banking Supervision (BCBS) replaced VaR with Expected Shortfall (ES), or Conditional VaR (CVaR), as the new primary measure for banking institutions to forecast market risk and hence allocate the relevant amount of regulatory market risk capital. ES measures the probability weighted losses beyond VaR, so VaR remains a crucial step in its computation and retains its significance in estimating market risk and associated measures. A Kalman filter is used for the first time to estimate both VaR (and ES) to provide an alternative technique to existing industry methods. Modelling the volatility of asset returns as a stochastic process, the Kalman filter uses Bayesian statistics to forecast unobservable data by identifying underlying patterns required to predict future values. Back-testing results (in which the number of times VaR or ES forecasted too low a value to cover the following day's market loss is compared with the prescribed confidence level) indicate that the Kalman filter is a reliable and robust contender in the volatility framework milieu, outperforming GARCH, EWMA and equally weighted measures of volatility in both volatile and calm market conditions.

Keywords

Kalman Filter, Value-at-Risk

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