## 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.

- Interest Rate Simulation & Forecasting: Using CIR (Cox Ingersoll Ross) Model: Introduction
- Interest Rate Simulation & Forecasting: Using CIR (Cox Ingersoll Ross) Model: Estimating Parameters & Calibrating the CIR Model
- Interest Rate Simulation & Forecasting: Using CIR (Cox Ingersoll Ross) Model: Simulating the term structure of interest rates
- Cox-Ingersoll-Ross (CIR) interest rate model – Parameter calibration, Short rates simulation and modeling of longer term interest rates – An example

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

- Interest Rate Simulation Models: Black, Derman and Toy (BDT): Building BDT in Excel: Introduction
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: Define Input Cells
- Interest Rate Simulation Models: Building Black, Derman and Toy (BDT) in Excel: Define Output Cells
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: Define Calculation Cells: Construct short rate binomial tree
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: Define Calculation Cells: Construct State Price Lattices
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: Define Calculation Cells: Calculate Prices from Lattice
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: Define Calculation Cells: Calculate Yields & Yield volatility from Lattice
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: Define & Set Solver Function & Results
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: How to utilize the results of a BDT interest rate model: Derivation of Short Rates
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: How to utilize the results of a BDT interest rate model: Pricing Bonds
- Interest Rate Simulation Models: Steps for building Black, Derman and Toy (BDT) model in Excel: How to utilize the results of a BDT interest rate model: Pricing Options

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.

- Interest Rate Simulation Modelling: HJM (Heath Jarrow Merton) Model: How to construct an Interest Rate Model in Excel – Define input cells
- Interest Rate Simulation Modelling: HJM (Heath Jarrow Merton) Model: How to construct an Interest Rate Model in Excel – Define calculation cells
- Interest Rate Simulation Modelling: HJM (Heath Jarrow Merton) Model: How to construct an Interest Rate Model in Excel – Determine Prices

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.

- Interest Rate Forecasting & Simulation: Principal Component Analysis (PCA) : Overview
- Interest Rate Forecasting & Simulation: Principal Component Analysis (PCA) : How to conduct a Principal Component Analysis in Excel: Data
- Interest Rate Forecasting & Simulation: Principal Component Analysis (PCA) : How to conduct a Principal Component Analysis in Excel: Covariance Matrix
- Interest Rate Forecasting & Simulation: Principal Component Analysis (PCA) : How to conduct a Principal Component Analysis in Excel: Eigenvectors
- Interest Rate Forecasting & Simulation: Principal Component Analysis (PCA) : How to conduct a Principal Component Analysis in Excel: Diagonal Matrix
- Interest Rate Forecasting & Simulation: Principal Component Analysis (PCA) : How to conduct a Principal Component Analysis in Excel: Solver Setup & Results