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The HJM framework has the advantage that it allows seamless extension from one to several sources of uncertainty. The choice of number of volatility factors to use is driven by a number of often conflicting considerations. Additional sources of uncertainty introduce additional degrees of freedom to the evolution of the term structure which allows decorrelation [...]

Principal component analysis (PCA) may be performed on a time series of historical term structure data in an attempt to identify the dominant factors driving its evolution. PCA produces factors maximising successive contributions to overall variance. Hence these factors attempt to explain the diagonal of the covariance matrix. The resulting factors are surrogate volatility factors [...]