Heath Jarrow Merton (HJM) Interest Rate Model - Package
About the Course
The course consists of three EXCEL files that illustrate the following:
- The derivation and construction of spot/ zero rate and forward rate term structures as follows:
- Par term structures are obtained from the interbank rates and treasury rates.
- Cash flows (coupon and principal payments) of coupon bearing bonds are determined from the par term structures.
- Cash flows are stripped so that each individual cash flow may be considered a zero coupon bond structure.
- Individual cash flows are discounted, summed and equated to the par values of bonds to determine the zero coupon curve (spot rate) term structure.
- Forward curve term structure is derived from bootstrapping the derived zero coupon curve term structure.
- A graphical illustration of the resulting spot and forward term structures is also given.
- The use of Principal Component Analysis (PCA) to determine the number of workable factors to explain volatility for the HJM interest rate model. This 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
- An example of the construction of a three factor HJM interest rate model in EXCEL that shows how the following are determined:
- Brownian Shocks using a normally scaled random number generator
- Drifts using the principal component factors for volatility of the forward rate term structure
- Spot & forward rates using the initial zero rate yield rates, principal component factors and total drift
- Price/ discount factors using the derived spot & forward rates
- True & Path bond prices
After taking this course you will be able to:
- Derive spot and forward rate term structures from the available interbank and treasury yield curves
- 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
- Calculate Brownian shocks
- Calculate the principal component factor based drifts
- Construct the HJM interest rate model comprising of a spot and forwards rates tree
- Calculate the discount factor or one-period price tree from the HJM interest rate model
- Calculate the value of a bond using the price tree
Knowledge of EXCEL, mathematics, probability and some familiarity of regression/ curve fitting analysis.
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.