An introduction to interest rate modelling

Interest rates affect all of our lives, from the money we have in our banks and the mortgages we pay on our houses, to the value that our future pension plans will have. The rates involved in all of these are derived from an ever-changing expectation of what interest rates will be in the future. Stochastic interest rate models can be used to make such predictions and are in widespread use across the financial sector.

In this talk we will begin with a brief introduction to the topic of interest rates. We will then consider two different approaches to interest rate modelling: that of modelling the short-term interest rate (i.e. the “short rate”) and forward interest rate. To illustrate modelling of the short rate we will present one of the most famous interest rate models: the Vasicek model [1]. We will solve the single factor version of this model and discuss its solution and shortcomings. We will address how these shortcomings can be overcome by extending this model to be a two-factor model, which we will again present and derive the solution to. Finally, as an example of a forward rate model we will present the LMM+ model, the current model of choice at Moody’s Analytics for the modelling of interest rates. We will discuss some key properties of this model, its calibration and its effectiveness in replicating financial market observables.

We will close this talk with an overview of the importance of interest rate models in the work that we carry out at Moody’s Analytics. These form the foundation on which our suite of stochastic economic models - the Economic Scenario Generator - is based.

References

[1] Vasicek, O. “An equilibrium characterization of the term structure”. Journal of Financial Economics 5, (1977) 177-188.