 # Interest Rate Simulation Crash Course

Interest Rate Simulation and Forecasting Models are  employed to value instruments which are dependent on interest rates as well as to value new hedge instruments.

Interest rate models are defined by state variables and their processes. Think of these are the primary drivers or factors behind a given phenomenon. Just like pressing the accelerator changes and impact speed of a vehicle, tweaking a model parameter or model variable changes the value being modeled.

The values taken by the state variables that constitute an interest model give the position or state of the item being model. The processes determine how the state variables change over time. Interest rate processes or changes in state variables are usually stochastic processes, i.e. they incorporate an element of randomness. These processes can usually be divided into a non-random deterministic component, called drift and a random, noise term called volatility.

The purpose of interest rate models crash course  is build an understanding of interest rate behavior.

Model processes may depend on the evolution of a single factor such as the short rate, as in the case of the CIR one factor equilibrium model. We start with the simplest of interest rate models, the Cox Ingersoll Ross interest rate simulator and review the model as well as the steps required in its calibration.

A slightly different application is used to illustrate the construction and calibration of the one factor no arbitrage Black, Derman and Toy (BDT) model

We then move towards more complicated Interest rate models that use multiple factors and require estimates as well as configuration of drift, volatility for multiple factors, as in the case of the Heath, Jarrow, Merton (HJM) no arbitrage model.

In order to determine a workable number of components / factors for the Heath, Jarrow, Merton (HJM) model, a principal component analysis (PCA) needs to be performed.