Interest Rate Modelling (Finance and Capital Markets Series)

ISBN: 1403934703
EAN: 2147483647

Year: 2004
Pages: 132

Authors: Simona Svoboda

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Table of Contents
BackCover
Interest Rate Modelling
Introduction
Approaches to term structure modelling
Outline of the book
Part I: Interest Rate Models
Chapter 1: The Vasicek Model
1.2 Term structure equation
1.3 Risk-neutral valuation
1.4 Note on empirical estimation of the market risk premium
1.5 Specific model
1.6 Conclusion
Appendix
Chapter 2: The Cox, Ingersoll and Ross Model
2.2 Equilibrium risk-free rate of interest
2.3 Equilibrium expected return on any contingent claim
2.4 Value of any contingent claim in equilibrium
2.5 A more specialised economy
2.6 Term structure model
2.7 Distribution of the interest rate
2.8 Bond pricing formula
2.9 Properties of the bond price under the CIR model
2.10 Extending the model to allow time-dependent drift
2.11 Comparison of the Vasicek and CIR methods of derivation
2.12 More complicated model specifications
2.13 Conclusion
Chapter 3: The Brennan and Schwartz Model
3.2 Specific models
3.3 Conclusion
Chapter 4: Longstaff and Schwartz-A Two-Factor Equilibrium Model
4.2 Equilibrium term structure
4.3 Option pricing
4.4 Conclusion
Chapter 5: Langetieg s Multi-Factor Equilibrium Framework
5.2 Choice of generating process
5.3 Multivariate elastic random walk
5.4 The bond pricing model
5.5 Conclusion
Chapter 6: The Ball and Torous Model
6.2 Brownian bridge process
6.3 Option valuation
6.4 Conclusion
Chapter 7: The Hull and White Model
7.2 Extension of the Vasicek model
7.3 Pricing contingent claims within the extended Vasicek framework
7.4 The extended Cox-Ingersoll-Ross model
7.5 Fitting model parameters to market data
7.6 Conclusion
Chapter 8: The Black, Derman and Toy One-Factor Interest Rate Model
8.2 Pricing contingent claims
8.3 Calibrating the lattice to an observed term structure
8.4 Continuous time equivalent
8.5 A fundamental flaw
8.6 Conclusion
Chapter 9: The Black and Karasinski Model
9.1 The lognormality assumption
9.2 Specification of the binomial tree
9.3 Matching the lognormal distribution
9.4 Conclusion
Chapter 10: The Ho and Lee Model
10.2 Binomial lattice specification
10.3 Arbitrage-free interest rate evolution
10.4 Relationship to Vasicek and CIR models
10.5 Pricing contingent claims
10.6 Conclusion
Chapter 11: The Heath, Jarrow and Morton Model
11.1 Initial specifications
11.2 Specifications of the various processes
11.3 Arbitrage-free framework
11.4 Eliminating the market prices of risk
11.5 The problem with forward rates
11.6 Unifying framework for contingent claim valuation
11.7 Ho and Lee model within the HJM framework
11.8 Comparison of equilibrium and arbitrage pricing
11.9 Markovian HJM model
11.10 Conclusion
Chapter 12: Brace, Gatarek and Musiela Model
12.2 Initial framework
12.3 Model of the forward LIBOR rate
12.4 Forward risk-neutral measure
12.5 Forward LIBOR rate with respect to the forward measure
12.6 Derivative pricing
12.7 Calibration to market volatilities
12.8 Conclusion
Part II: Calibration
Chapter 13: Calibrating the Hull-White extended Vasicek approach
13.1 Using information from the observed term structure of interest rates and volatilities
13.2 Call option on a coupon paying bond
13.3 Using market data
13.4 Cubic spline interpolation
13.5 Constant mean reversion and volatility parameters
13.6 Flat volatility term structure
13.7 Calibration methodology
Appendix Cubic Spline Interpolation
Cubic Bessel Interpolation
Integrating the inverse of the square of a cubic polynomial
Chapter 14: Calibrating the Black, Derman and Toy discrete time model
14.1 Initial Term Structure
14.2 Calibrating to interest rate term structure only
14.3 Forward Induction: making use of state prices
14.4 Pricing contingent claims - Backward Induction
14.5 Calibration methodology for a constant volatility parameter
Chapter 15: Calibration of the Heath, Jarrow and Morton framework
15.1 Volatility Function Specifications
15.2 Implied Volatility Specification
15.3 Historical Volatility Specification
15.4 Principal Component Analysis
15.5 Choosing the number of volatility factors
15.6 Combining Historical and Implicit Calibration
Closing Remarks
Bibliography
Index
Index_B
Index_C
Index_D
Index_E
Index_F
Index_G
Index_H-K
Index_L
Index_M
Index_N
Index_O
Index_P-Q
Index_R
Index_S
Index_T-U
Index_V-Z
List of Figures
List of Assumptions