Principal Component Analysis – PCA – US Treasury Yield Rates

About the Course

This course consists of an EXCEL file which illustrates how Principal Component Analysis is used to determine the number of workable factors or principal components (PCs) of volatility for the underlying US Treasury yield rates term structure.

Derived PCs for a forward rate term structure are used as inputs to the Heath-Jarrow-Merton (HJM) interest rate model (not illustrated in this course).

The file includes:

• Data selection from given dataset
• Construction of the Covariance, eigenvector and diagonal matrices
• Setting up and running of Solver functionality to obtain solutions for eigenvectors and eigenvalues
• Determination of number of component/ factors to be used in the HJM model
• Determination of functional forms for selected eigenvectors
• Determination of weights for functional forms through derived volatility calibration

Learning objectives

After taking this course you will be able to:

• Compute the principal components (eigenvectors) and their relative importance factors (eigenvalues) for the underlying term structure using EXCEL’s matrix multiplication, inverse matrix & Solver functionalities
• Determine functions for the selected eigenvectors/ principal components
• Calculate the scaling factor for each component function’s so that the combined volatilities derived from these functions match the volatilities inherent in the underlying term structure

Prerequisite

Knowledge of EXCEL, mathematics and some familiarity of regression/ curve fitting analysis.

Target Audience

The course is aimed at individuals responsible for the pricing of money market, derivatives and structured products as well as those involved in asset liability management and risk management, including the simulation and stress testing of rate sensitive asset and liability portfolios within banks, insurance companies and mutual funds.