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Writing out the 3-factor (3F) generalisation of the 1F Vasicek model (i.e. write out the autonomous Ornstein-Uhlenbeck SDE's), write a brief 1-page Technical Note which describes
1. how the 3F generalisation improves upon the 1F Vasicek model, and
2. how the first two latent factors can be shown to be consistent with the 'level' and 'slope' or 'twist' effects which result from a Principal Compo- nents analysis (PCA) of movements in the yield curve of spot rates over historical time.
Hint Part 2.
First explain why the 'long yield' (30Y spot rate, for example) is a good proxy for the 'prevailing level' of the yield curve over time, and hence a good proxy for the 'level' factor in PCA,
Second explain why in referring to the 'slope' or 'twist' effect, PCA factor sensitivity outputs typically show that most of the empirically observed 'twist effect' occurs at the short end of the yield curve (why is this ?)
Descriptive statistics was normally used to assess the distribution of the variables taken into consideration. if the variables are continuous, then mean, median and other descriptive measures were used to identify the distribution. on the other hand, if the variable is qualitative, then, frequency distribution was used to assess the distribution for the same.
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