1.Introduction
2.Arbitrage,Martingales and Numerical Methods
2.1 Arbitrage and Martingales
2.1.1 Basic Setup
2.1.2 Equivalent Martingale Measure
2.1.3 Change of Numeralre Theorem
2.1.4 Girsanov'S Theorem and Ito'S Lemma
2.1.5 Application:Black.Scholes Model
2.1.6 Application:Foreign-ExchangeOptions
2.2 Numerical Metbods
2.2.1 Derivation of Black-Scboles Partial Differential
Equation
2.2.2 Feynman-Kac Formula
2.2.3 Numerical Solution of PDE'
2.2.4 Monte Carlo Simulation
2.2.5 Numerical Integration
Part Ⅰ. Spot and Forward Rate Models
3. Spot and Forward Rate Models
3.1 Vasicek Methodology
3.1.1 Spot Interest Rate
3.1.2 Partial Differential Equation
3.1.3 Calculating Prices
3.1.4 Example:Ho-Lee Model
3.2 Heath-Jarrow-Morton Methodology
3.2.1 Forward Rates
3.2.2 EQuivalent Martingale Measure
3.2.3 Calculating Prices
3.2.4 Example:Ho-LeeModel
3.3 E quivalence of the Methodologies
4. Fundamental Solutions and the Forward-Risk-Adjusted
Measure
4.1 Forward-Risk-Adjusted Measure
4.2 Fundamental Solutions
4.3 Obtaining Fundamental Solutions
4.4 Example:Ho-Lee Model
4.4.1 Radon-Nikodym Derivative
4.4.2 Fundamental Solutions
4.5 Fundamental Solutions for Normal Models
5. TheHull-White Model
5.1 Spot Rate Process
5.1.1 Partial Difierential Equation
5.1.2 Transformation of Variables
5.2 Analytical Formulae
5.2.1 Fundamental Solutions
5.2.2 OptionPrices
5.2.3 Pricesfor Other Instruments
5.3 Implementation oftheModel
5.3.1 Fitting the Model to the Initial Term-Structure
5.3.2 Transformation ofVariables
5.3.3 Trinomial Tree
5.4 Performance ofthe Algorithm.
5.5 Appendix
6. The Squared Gatmsian Model
6.1 Spot Rate Process
6.1.1PartialDifferential Equation
6.2 AnaIytical Formulm
6.2.1 Fundarnental Solutions
6.2.2 Option Prices
6.3 Implementation of the Model
6.3.1 Fitting the Model to the Initial Term-Structure
6.3.2 ninomial Tree
6.4 Appendix A
6.5 Appendix B
7. An Empirical Comparison of 0ne-Factor Models
7.1 Yield-Curve Models
7.2 Econometric Approach
7.3 Data
7.4 Empirical Results
7.5 Conclusions
Part Ⅱ. Market Rate Models
8. LIBOR and Swap Market Models
8.1 LIBOR Market Models
8.1.1 LIBOR Process
8.1.2 Caplet Price
8.1.3 Terminal Measure
8.2 Swap Market Models
8.2.1 Interest Rate Swaps
8.2.2 Swaption Price
8.2.3 Terminal Mcaste
8.2.4 T1-Forward Measure………
8.3 Monte Carlo Simulation for LIBOR Market Models
8.3.1 Calculating the Numeralre Rebased Payoff
8.3.2 Example:Vanilla Cap
8.3.3 Diserete Barrier Caps/Floors
8.3.4 Discrete Barrier Digital Caps/Floors
8.3.5 Payment Stream
8.3.6 Ratchets
8.4 Monte Carlo Simulation for Swap Market Models
8.4.1 Terminal Measure
8.4.2 T1-Forward Measure
8.4.3 Example:Spread Option
9. Markov-Funetional Models
9.1 Basic Assumptions
9.2 LIBOR Markov-Functional Model
9.3 Swap Markov-Functional Model
9.4 Numerical Implementation
9.4.1 Numerical Integration
9.4.2 Non-Parametric Implementation
9.4.3 Semi-Parametric Implementation
9.5 Forward Volatilities and Auto-Correlation
9.5.1 Mean-Reversion and Auto-Correlation
9.5.2 Auto-Correlation and the Volatility Function
9.6 IBOR Example:Barries Caps
9.6.1 Numefical CaIculation
9.6.2 Comparison with LIBOR Market Model
9.6.3 Impact of Mean-Reversion
9.7 LIBOR Example:Chooser-andAuto-Caps
9.7.1 Auto-Caps/Floors
9.7.2 Chooser-Caps/Floors
9.7.3 Auto-and Chooser-Digitals
9.7.4 Numerical Implementation
9.8 Swap Example:Bermudan Swaptions
9.8.1 Early Notification
9.8.2 Comparison BetweenMoriels
10. An Empirical Comparison of Market Models
10.1 Data Description
10.2 LIBOR Market ModeI
10.2.1 Calibration Methodology
10.2.2 Estimation and Pricing Results
10.3 Swap Market Model
10.3.1 Calibration Methodology
10.3.2 Estimationand Pricing Resuits
10.4 Conclusion
11. Convexity Correction
11.1 Convexity Correction and Change of Numeraire
11.1.1 Multi-urrency Change of Numeraire Theorem
11.1.2 Convexity Correction
11.2 Options on Convexity Corrected Rares
11.2.1 Option Price Formula
11.2.2 Digital Price Formula
11.3 SingleIndex Products
11.3.1 LIBOR in Arrears
11.3.2 Constant Maturity Swap
1l.3.3 Diffed LIBOR
11.3.4 Diffed CMS
11.4 Multi-Index Products
11.4.1 Rate Based Spreadoptions
1l.4.2 Spread Digital
11.4.3 Other Multi-ndex Products
11.4.4 Comparisonwith Market Models
11.5 A Warning on Convexity Correction
11.6 Appendix:Linear Swap Rate Model
12. Extensions and Further Developments
12.1 General Philosophy
12.2 Multi-actor Models
12.3 V0latility Skews
References
Index