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A factor analysis of volatility across the term structure: the Spanish case
Alfonso Novales and Sonia Benito |
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A major problem for risk management in fixed income portfolios is the large dimensionality of the implied vector interest rate. This is especially important for VAR computation, for which an estimate of the variance-covariance matrix of interest rates needed. Alexander (2000) suggested computing that matrix from a factor model for interest rates, sharply reducing the dimensionality of the problem. We start by showing that the term structure of volatilities for zero-coupon interest rates from the Spanish secondary debt market can also be explained by a reduced number of factors. This factor representation can be used to product volatility time series across the whole term structure that are shown to significantly differ from those obtained under Alexander’s approach. Furthermore, the latter is shown to underperform our alternative proposal, which is similar to the ad-hoc estimation rules in Riskmetrics. Reducing the dimensionality of the vector interest rates seems to lead to a relevant loss of information regarding second order moments that does not occur in alternative approaches that use the information in the full vector.
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