Interest Rate Modeling for Risk Management presents an economic model which can be used to compare interest rate and perform market risk assessment analyses. The key interest rate model applied in this book is specified under real-world measures, and the result is used as to generate scenarios for interest rates. The book introduces a theoretical framework that allows estimating the market price of interest rate risk. For this, the book starts with a brief explanation of stochastic analysis, and introduces interest rate models such as Heath-Jarrow-Morton, Hull-White and LIBOR models. The real-world model is then introduced in subsequent chapters. Additionally, the book also explains some properties of the real-world model, along with the negative price tendency of the market price for risk and a positive market price of risk (with practical examples). Readers will also find a handy appendix with proofs to complement the numerical methods explained in the book.
This book is intended as a primer for practitioners in financial institutions involved in interest rate risk management. It also presents a new perspective for researchers and graduates in econometrics and finance on the study of interest rate models.
The second edition features an expanded commentary on real world models as well as additional numerical examples for the benefit of readers.
Table of Contents
1 Interest Rate Risk
1.1 Interest Rate And Discount Factor
1.2 Swap Rate And Forward Libor
1.3 Term Structure Of Interest Rates
1.4 Interest Rate Risk Of Bonds
1.5 Value At Risk
1.6 Computing Var
1.6.1 Covariance Var Models
1.6.2 Historical Simulation Models
1.6.3 Monte Carlo Simulation Models
1.6.4 Nested Simulation
1.7 Validity Of Var
2 Fundamentals Of Stochastic Analysis
2.1 Probability Space
2.2 Random Variables
2.3 Stochastic Process
2.4 Martingales And Conditional Expectation
2.5 Stochastic Integral
2.6 Stochastic Di Erential Equation
2.7 Multi-Dimensional Stochastic Process
3 Arbitrage Theory
3.1 Arbitrage Pricing
3.2 Change Of NumEraire
3.3 Market Price Of Risk
4 Heath Jarrow Morton Model
4.1 Heath-Jarrow-Morton Framework
4.2 Arbitrage Pricing And Market Price Of Risk
4.3 Volatility And Principal Components
4.4 The Hull{White Model
4.5 Var Computed In The Real-World
4.6 Estimation Of The Market Price Of Risk
5 Libor Market Model
5.1 Libor Market Model
5.2 Existence Of Libor Market Model
5.3 Libor Market Model Under A Real-World Measure
5.4 Spot Libor Model
5.5 PK Measure Model
6 Real-World Model In The Gaussian Hjm Model
6.1 Discretization Of Forward Rate Process
6.2 Estimation Of Market Price Of Risk
6.3 Market Price Of Risk: State Space Setup
6.4 Historical Trend Of Forward Rate
6.5 Market Price Of Risk And The Trends
6.6 Interpretation Of Market Price Of Risk
6.7 Property Of Real-World Simulation
6.8 Simulation Model In State Space
6.9 Numerical Procedure
7 Remarks On Real-World Models
7.1 Di Erences Between Real-World And Risk-Neutral Models
7.2 Negative Price Tendency Of Market Price Of Risk
7.2.1 Flat Yield Model
7.2.2 Negative Price Tendency
7.2.3 Positive Slope Model
7.3 Mean Price Property Of The Market Price Of Risk
7.4 Assumption Of Constant Market Price Of Risk
7.5 Application To Counterparty Credit Risk
8 Real-World Model In The Hull White Model
8.1 Volatility Estimation
8.2 Historical Volatility Of The Short Rate
8.3 Historical Volatility Of Forward Rate
8.4 Real-World Modeling
8.5 Simulation Model
8.6 Numerical Procedure
9 Real-World Model In The Libor Market Model
9.1 Discretization Of Libor Process
9.2 Estimation Of The Market Price Of Risk
9.3 State Space Setup
9.4 Historical Trends Of Libor
9.5 Qualitative Estimate Of Market Price Of Risk
9.6 Fundamental Properties Of Simulation
9.7 Real-World Model In State Space
9.8 Dimensionality Reduction
9.8.1 Setup Of Dimensionality Reduction
9.8.2 Dimensionality Reduction
9.8.3 Dimensionality Reduction In Practice
9.9 Numerical Procedures In Lmrw
10 Numerical Examples
10.1 Real-World Model In The Gaussian Hjm Model
10.1.1 Estimation Of Market Price Of Risk
10.1.2 Observation On Simulation
10.2 Libor Market Model
10.2.1 Estimation Of Market Price Of Risk
10.2.2 Four Cases: Cases B1 To B4
10.2.3 Examination Of Four Cases
10.3 Positive Market Price Of Risk
10.4 Negative Price Tendency
10.5 Mean Price Property
10.6 Credit Exposure Calculation
10.6.1 Interest Rate Swap
10.6.2 Numerical Conditions
10.6.3 Distribution Of Swap Value
10.6.4 Credit Exposure Calculation
A Basics Of Numerical Analysis
A.1 Normal Distribution
A.2 Eigenvalues And Eigenvectors
B Principal Component Analysis
B.1 Principal Component
B.2 Principal Component Space
B.3 Covariance And Volatility
C Maximum Likelihood Estimation
D Proofs For Dimension Reduction
D.1 Proof Of Proposition
D.2 Proof Of Theorem
Author
Takashi Yasuoka
