Interest Rate Modeling for Risk Management: Market Price of Interest Rate Risk, Second Edition
by Takashi Yasuoka  (Author)

About the Author
Takashi Yasuoka, Professor, Graduate School of Engineering Management, Shibaura Institute of Technology.

About this book
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.

Brief contents
1 INTEREST RATE RISK 1
    1.1 Interest Rate and Discount Factor 2
    1.2 Swap Rate and Forward LIBOR 6
    1.3 Term Structure of Interest Rates 8
    1.4 Interest Rate Risk of Bonds 10
    1.5 Value at Risk 14
    1.6 Computing VaR 18
        1.6.1 Covariance VaR Models 19
        1.6.2 Historical Simulation Models 21
        1.6.3 Monte Carlo Simulation Models 22
        1.6.4 Nested Simulation 23
    1.7 Validity of VaR 25
2 FUNDAMENTALS OF STOCHASTIC ANALYSIS 31
    2.1 Probability Space 32
    2.2 Random Variables 34
    2.3 Stochastic Process 36
    2.4 Martingales and Conditional Expectation 39
    2.5 Stochastic Integral 44
    2.6 Stochastic Differential Equation 45
    2.7 Multi-dimensional Stochastic Process 50
3 ARBITRAGE THEORY 53
    3.1 Arbitrage Pricing 54
    3.2 Change of Num′eraire 56
    3.3 Market Price of Risk 61
4 HEATH–JARROW–MORTON MODEL 65
    4.1 Heath-Jarrow-Morton Framework 66
    4.2 Arbitrage Pricing and Market Price of Risk 70
    4.3 Volatility and Principal Components 74
    4.4 The Hull–White Model 79
    4.5 VaR Computed in the Real-world 84
    4.6 Estimation of the Market Price of Risk 86
5 LIBOR MARKET MODEL 91
    5.1 LIBOR Market Model 92
    5.2 Existence of LIBOR Market Model 94
    5.3 LIBOR Market Model under a Real-world Measure 96
    5.4 Spot LIBOR Model 103
    5.5 Pk Measure Model 106
6 REAL-WORLD MODEL IN THE GAUSSIAN HJM MODEL 111
    6.1 Discretization of Forward Rate Process 112
    6.2 Estimation of Market Price of Risk 114
    6.3 Market Price of Risk: State Space Setup 119
    6.4 Historical Trend of Forward Rate 124
    6.5 Market Price of Risk and the Trends 129
    6.6 Interpretation of Market Price of Risk 134
    6.7 Property of Real-world Simulation 139
    6.8 Simulation Model in State Space 142
    6.9 Numerical Procedure 146
7 REMARKS ON REAL-WORLD MODELS 149
    7.1 Differences between Real-world and Risk-neutral Models 150
    7.2 Negative Price Tendency of Market Price of Risk 153
        7.2.1 Flat Yield Model 153
        7.2.2 Negative Price Tendency 154
        7.2.3 Positive Slope Model 158
    7.3 Mean Price Property of the Market Price of Risk 161
    7.4 Assumption of Constant Market Price of Risk 166
    7.5 Application to Counterparty Credit Risk 170
8 REAL-WORLD MODEL IN THE HULL–WHITE MODEL 175
    8.1 Volatility Estimation 176
    8.2 Historical Volatility of the Short Rate 178
    8.3 Historical Volatility of Forward Rate 180
    8.4 Real-world Modeling 186
    8.5 Simulation Model 189
    8.6 Numerical Procedure 192
9 REAL-WORLD MODEL IN THE LIBOR MARKET MODEL 195
    9.1 Discretization of LIBOR Process 196
    9.2 Estimation of the Market Price of Risk 198
    9.3 State Space Setup 204
    9.4 Historical Trends of LIBOR 208
    9.5 Qualitative Estimate of Market Price of Risk 211
    9.6 Fundamental Properties of Simulation 214
    9.7 Real-world Model in State Space 220
    9.8 Dimensionality Reduction 224
        9.8.1 Setup of Dimensionality Reduction 225
        9.8.2 Dimensionality Reduction 226
        9.8.3 Dimensionality Reduction in Practice 228
    9.9 Numerical Procedures in LMRW. 229
10 NUMERICAL EXAMPLES 235
    10.1 Real-world Model in the Gaussian HJM Model 237
        10.1.1 Estimation of Market Price of Risk 237
        10.1.2 Observation on Simulation 243
    10.2 LIBOR Market Model 246
        10.2.1 Estimation of Market Price of Risk 246
        10.2.2 Four Cases: Cases B1 to B4 248
        10.2.3 Examination of Four Cases 251
    10.3 Positive Market Price of Risk 255
    10.4 Negative Price Tendency 261
    10.5 Mean Price Property 265
    10.6 Credit Exposure Calculation 270
        10.6.1 Interest Rate Swap 270
        10.6.2 Numerical Conditions 271
        10.6.3 Distribution of Swap Value 273
        10.6.4 Credit Exposure Calculation 276
A BASICS OF NUMERICAL ANALYSIS 279
    A.1 Normal Distribution 279
    A.2 Eigenvalues and Eigenvectors 280
B PRINCIPAL COMPONENT ANALYSIS 283
    B.1 Principal Component 283
    B.2 Principal Component Space 284
    B.3 Covariance and Volatility 286
C MAXIMUM LIKELIHOOD ESTIMATION 289
D PROOFS FOR DIMENSION REDUCTION 293
    D.1 Proof of Proposition 9.8.1 293
    D.2 Proof of Theorem9.8.2 294
References 297
Author Index 303
Subject Index 305

Series: Economics: Current and Future Developments (Book 1)
Pages: 322 pages
Publisher: Bentham Science Publishers (May 9, 2018)
Language: English
ISBN-10: 1681086905
ISBN-13: 978-1681086903