EVT-based Estimation Of VaR And CVaR

The large increase in the number of traded assets in the portfolio of most financial institutions has made the measurement of market risk a primary concern for regulators and for internal risk control. After being proposed in 1993, Value-at-Risk (VaR) approach has become the standard for risk management industry. But VaR has various theoretical deficiencies as a measure of market risk. Conditional VaR (CVaR) is an alternative risk measure to the quantile which overcomes the theoretical deficiencies of VaR. In particular, this risk measure gives some information about the size of the potential losses given that a loss bigger than VaR has occurred. This paper estimates and assesses tail-related risk using VaR and CVaR together.Though VaR and CVaR have many compute methods, they have limitations. Because almost all of the traditional methods estimating tail-related risk VaR and CVaR focus on the central observations or, in other words, on returns under normal market conditions. However, VaR and CVaR are risk measures that relates solely to the tails of the distribution. The extreme values which lies in the tail are some rarely happened events that have significant influence. Extreme Value Theory (EVT) is the statistical model to study the behavior of extreme values. This paper introduces the basic knowledge of EVT and estimates VaR and CVaR using EVT. Combining with heteroscedastic model, EVT can estimate VaR and CVaR more accurately.The application methods of EVT have block maximum method and peak over threshold method according to related ways of identifying extremes in real data. Because peak over threshold method has difficulties in choosing threshold, this paper studys block maximum method for estimate VaR and CVaR. Indeed the research about block maximum method for estimate CVaR has not been found. This paper gains the formulas computing VaR and CVaR using block maximum method. Based on the stock data of S&P 500 index. this paper makes an empirical analysis of VaR and CVaR estimation using block maximum method of EVT. Empirical findings conclude that block maximum method can well approximate the tail of financial return distribution. Backtesting indicates block maximum method can accurately estimate VaR and CVaR for high probability excess 95%.