Abstract:

Under the assumption that the yield series is a strictly stationary process, we present an equation satisfied by value at risk (VaR) at time t given historical data and an analytic formula for conditional value at risk (CVaR). We use S&P 500 as an example to discuss how the length of historical data before t affects the estimate of VaR and CVaR at time t . The VaR series obtained with the proposed method and that with the GARCH model are compared. It is found that both results have similar fluctuations, but VaR values of the former is larger and smoother because normality assumption is not used. By using different sample length to estimate CVaR, the proposed method is shown to be more robust.

Key words: conditional density of stationary process, conditional value at risk (CVaR), kernel estimate

value at risk (VaR)