# Heath Jarrow Merton (HJM) Interest Rate Model – Topic Guide

The processes determine how the state variables change over time. Model processes may depend on the evolution of a single factor or multiple factors. The HJM interest rate no-arbitrage model is an example of the latter.

**EXCEL files**

The HJM interest rate model course is a pre-packaged deal of 3 EXCEL files that cover the following concepts:

- Zero Coupon and Forward Rates Term Structures derivation and construction (pre-requisite)
- Principal Component Analysis (PCA) used to determine the number of workable factors for the HJM interest rate model. This includes:
- Data selection and adjustment
- Construction of the Covariance, eigenvector and diagonal matrices
- Set 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
- Example of the construction of a three factor HJM interest rate model in EXCEL. This includes:
- The definition of input cells (e.g. initial yield (zero) rates and the volatility functions),
- The definition of calculation cells (e.g. Brownian shocks, drifts, forwards and spot rates) and
- The definition of output cells (e.g. price matrix, path prices and true prices)

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