Lixin Wu

Interest Rate Modeling

Theory and Practice

• Gebundenes Buch

Produktbeschreibung

Containing many results that are new, or which exist only in recent research articles, this thoroughly revised third edition of this book portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation.

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Produktdetails

• Verlag: CRC Press
• 3rd edition
• Seitenzahl: 425
• Erscheinungstermin: 27. August 2024
• Englisch
• Abmessung: 239mm x 166mm x 30mm
• Gewicht: 773g
• ISBN-13: 9781032483559
• ISBN-10: 1032483555
• Artikelnr.: 70151820

Autorenporträt

Lixin Wu earned his PhD in applied mathematics from UCLA in 1991. Originally a specialist in numerical analysis, he switched his area of focus to financial mathematics in 1996. Since then, he has made notable contributions to the area. He co-developed the PDE model for soft barrier options and the finitestate Markov chain model for credit contagion. He is, perhaps, best known in the financial engineering community for a series of works on market models, including an optimal calibration methodology for the standard market model, a market model with square-root volatility, a market model for credit derivatives, a market model for in inflation derivatives, and a dual-curve SABR market model for post-crisis derivatives markets. He also has made valuable contributions to the topic of xVA. Over the years, Dr. Wu has been a consultant for financial institutions and a lecturer for Risk Euromoney and Marco Evans, two professional education agencies. He is currently a full professor at the Hong Kong University of Science and Technology.

Inhaltsangabe

1. The Basics of Stochastic Calculus. 1.1. Brownian Motions. 1.2.
Stochastic Integrals. 1.3. Stochastic Differentials and Ito's Lemma. 1.4.
Multi-Factor Extensions. 1.5. Martingales. 1.6. Feynman-Kac Theorem. 2. The
Martingale Representation Theorem. 2.1. Changing Measures with Binomial
Models. 2.2. Change of Measures under Brownian Filtration. 2.3. The
Martingale Representation Theorem. 2.4. A Complete Market with Two
Securities. 2.5. Replicating and Pricing of Contingent Claims. 2.6.
Multi-Factor Extensions. 2.7. A Complete Market with Multiple Securities.
2.8. Notes. 3. U.S. Fixed-Income Markets. 3.1. The U.S. Federal Fund
Market. 3.2. The U.S. Bond Markets. 3.3. Bond Mathematics. 3.4. Discount
Curve and Zero-Coupon Yields. 3.5. Yield-Based Bond Risk Management. 3.6.
The Interbank Lending Market. 3.7. The LIBOR Market. 3.8. Repurchasing
Agreement. 4. LIBOR Transition and SOFR Derivatives Markets. 4.1. LIBOR
Scandal and the Cessation of LIBOR. 4.2. SOFR. 4.3. Transition to Risk-Free
Overnight Rates and LIBOR Fallbacks. 4.4. Linear Derivatives Based on the
Risk-Free Rates. 4.5. Nonlinear Derivatives Based on the Risk-Free Rates.
5. Forward Measures and the Black Formula. 5.1. Lognormal Model: The
Starting Point. 5.2. Forward Prices. 5.3. Forward Measure. 5.4. Black's
Formula for Call and Put Options. 5.5. Numeraires and Change of Measures.
5.6. Futures Price and Futures Rate. 6. The Heath-Jarrow-Morton Model.
6.1. The HJM Model. 6.2. Estimating the HJM Model from Yield Data. 6.3. An
Example of a Two-Factor Model. 6.4. Monte Carlo Implementations. 6.5.
Special Cases of the HJM Model. 6.6. Linear Gaussian Models. 6.7. Pricing
SOFR Derivatives under HJM Model. 6.8. Notes. 7. Short-Rate Models and
Lattice Implementation. 7.1. From Short-Rate Models to Forward-Rate Models.
7.2. General Markovian Models. 7.3. Binomial Trees of Interest Rates. 7.4.
A General Tree-Building Procedure. 8. Affine Term Structure Models. 8.1. An
Exposition with One-Factor Models. 8.2. Analytical Solution of Riccarti
Equations. 8.3. Pricing Options on Coupon Bonds. 8.4. Distributional
Properties of Square-Root Processes. 8.5. Multi-Factor Models. 8.6. Pricing
SOFR Futures under ATSMs. 8.7. Swaption Pricing under ATSMs. 8.8. Notes.
9. Market Model for SOFR Derivatives. 9.1. Market Model with SOFR Forward
Term Rates. 9.2. Construction of the Initial Forward Rate Curve. 9.3. Monte
Carlo Simulation Method. 9.4. Volatility Smiles and the Direct Adaptation
of Smile Models. 10. Convexity Adjustments. 10.1. Pricing through
Adjustments. 10.2. Quanto Derivatives. 11. Market Models with Stochastic
Volatilities. 11.1. SABR Model. 11.2. Wu and Zhang Model. 11.3. Appendix:
Derivation of the HKLW Formula. 11.4. Appendix: Proof of Proposition. 12.
Lévy Market Model. 12.1. Introduction to Lévy Processes. 12.2. Lévy-HJM
Model. 12.3. Market Model under Lévy Processes. 13. Market Model for
Inflation Derivatives. 13.1. CPI Index and Inflation Derivatives Market.
13.2. Rebuilt Market Model and the New Paradigm. 13.3. Pricing Inflation
Derivatives. 13.4. Model Calibration. 13.5. Smile Modeling. 14. Market
Model for Credit Derivatives. 14.1. Pricing of Risky Bonds: A New
Perspective. 14.2. Forward Spreads. 14.3. Two Kinds of Default Protection
Swaps. 14.4. Par CDS Rates. 14.5. Implied Survival Curve and Recovery-Rate
Curve. 14.6. Black's Formula for Credit Default Swaptions. 14.7. Market
Model with Forward Hazard Rates. 14.8. Pricing of CDO Tranches under the
Market Model. 14.9. Notes. 15. xVA: Definition, Evaluation, and Risk
Management. 15.1. Pricing through Bilateral Replications. 15.2. The Rise of
Other xVA. 15.3. Examples. 15.4. Notes.