## Heath Jarrow Merton (HJM) Interest Rate Model

**Heath Jarrow Merton (HJM) Interest Rate Model**

Interest rate simulation and forecasting models are employed to value instruments which are dependent on interest. Interest rate models are defined by state variables and their processes. The values taken by the state variables give the position or state of the item being model.

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)