# Interest Rate Simulation Crash Course – Detailed Course Description

### 1. Course Content

1. INTRODUCTION

a. Equilibrium vs. No-Arbitrage models
b. One- factor vs. multiple-factor models

2. BASIC CONCEPTS
a. Cash flows
b. Discounting Cash flows
c. Spot Rates
d. Forward Rates
e. Short rates
f. Yield to Maturity
g. Term structure of interest rates

3. DERIVATION OF THE ZERO AND FORWARD CURVES
a. Defining the Par Term Structure

• Step 1: Select an appropriate term structure
• Step 2: Extending the term structure
• Step 3: Creating a default term structure

b. Deriving the Zero Curve

• Step 1: Develop the cash flows matrix
• Step 2: Developing the discounted value of cash flows matrix and the zero curve

c. Deriving the Forward Curve

• Step 1: Deriving forward rates

4. BUILDING EQUITIES, COMMODITIES, CURRENCIES & INTEREST RATE MONTE CARLO SIMULATORS IN EXCEL
a. What is a Monte Carlo Simulator
b. The process or generator function for the MC simulator – a first pass
c. Building your first Monte Carlo (MC) Simulator model
d. Extending MC simulation models to Currencies & Commodities
e. MC Simulations models – Understanding drift and diffusion and volatility drag

• The Zero Drift, Zero Diffusion case
• The Unit Drift, Zero Diffusion case
• The Zero Drift, Unit Diffusion case
• The Unit Drift, Unit Diffusion case
• Understanding Volatility drag or ½ sigma2 (squared)

f. Linking Monte Carlo Simulation with Binomial Trees and the Black Scholes model
g. Simulating Interest rates using CIR and HJM

5. ONE-FACTOR MODELS
a. Cox Ingersoll Ross (CIR)

• ModelEstimating Parameters and Calibrating the CIR
• ModelSimulating future short term interest rates under the CIR
• ModelModelling longer term rates

b. Black Derman Toy (BDT) Model

• How to Construct a BDT Model in Excel

6. MULTIPLE FACTOR MODELS
a. PCA Analysis
i. The PCA Process- Overview
ii. How to conduct a Principal Component Analysis in Excel
b. HJM Model
i. Structure of an HJM Interest Rate Model
ii. How to construct an HJM interest Rate Model in Excel

7. MONTE CARLO SIMULATION APPLICATION: FORECASTING MONETARY POLICY RATE DECISION FOR PAKISTAN
a. Process
b. Results

• Step 1: Simulating Crude Oil Prices
• Step 2: Calculating Imports
• Step 3: Simulating Exports
• Step 4: Simulating Remittances
• Step 5: Calculating the change in Net Foreign Assets (NFA)
• Step 6: Calculating M2 and M2 Growth
• Step 7: Forecasting Core Inflation
• Step 7: Calculating the cut in the policy discount rate

BIBLIOGRAPHY

### EXCEL Examples

Yes – Available for sale

Construction of BDT
The example illustrates a BDT model constructed in Excel including input cells (initial yield rate and initial volatility), calculated cells (short rate and price lattices), defined solver functionality and output/ result cells (median rate and sigma).

How to utilize the results of the BDT model
The example illustrates how the BDT model results are used to value bond and option prices.

### 2. Introduction

Interest rates tend to fluctuate on a day to day basis as well as occasionally when there is a regime shift. These changes can signify a significant risk to those portfolios/ instruments whose values are derived from movements in the interest rate. Over the years many tools and products have been created that seek to hedge against or reduce and /or control such risk.

Models are usually employed in order to value instruments which are dependent on interest rates as well as to value the new hedge instruments.

Models are defined by state variables and their processes. The values taken by the state variables that constitute a 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 therefore is firstly to understand interest rate behaviour. By being able to study the distributional and statistically properties of interest rate movements such as the width of the distribution, its shape, the likelihood of reaching certain levels, etc, the risk manager is better able to discern interest rate movements, determine the likely range of future values and estimate the probabilities of losing more that a given amount. Understanding the movements helps in setting acceptable limits; helps in setting economic policy; helps in valuing financial instruments more reliably or hedging them more effectively.