Journal of Risk

Risk.net

Value-at-risk using the factor-ARCH model

Charlotte Christiansen

ABSTRACT

In this paper a modification of the factor-ARCH model proposed by Engle, Ng, and Rothschild (1990) is used to calculate the value-at-risk (VaR) of portfolios of Danish zero-coupon bonds. The factors are constructed as orthogonal portfolios of the bonds (denoted factor representing portfolios) using principal components analysis. The returns of the factor representing portfolios are assumed to be described by the univariate GARCH(1,1) model. The VaR is estimated in a two-factor setting for a number of zero-coupon bond portfolios, and these VaR quantities are compared to actual losses. The calculated VaR amounts are also compared to the RiskMetrics estimates.

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