Principal Component Analysis Applied to Forward rates I: Experiments with Empirical Data

Abstract

In this paper, we perform an estimation of the volatility of the forward rate using the Fourier method proposed by Malliavin and Mancino [4], together with the classical Principal Component Analysis. We have observed similar anomaly with the one in Liu [2]. We also give a remark on the practical use of the Malliavin-Mancino method.

Affine term structure as multi-soliton

“…In real market, however, the term structure of spot rates behaves nicer. According to the series of studies by N.L.Liu and her collaborators [1][2][3], from the term structure of spot rates only two or three factors up to almost 99% are detected when applied a principal component analysis (or its variants), while that of forward rates exhibits more than 10, sometimes 15, or even more factors. Much more straightforward peculiarity is that the samples of the term structure of forward rates often have more humps than those of spot rates.…”