Interest Rate Modeling

Lixin Wu is an associate professor at the Hong Kong University of Science and Technology. Best known in the financial engineering community for his work on market models, Dr. Wu co-developed the PDE model for soft barrier options and the finite-state Markov model for credit contagion.

• The Basics of Stochastic Calculus Brownian Motion Stochastic Integrals Stochastic Differentials and Ito’s Lemma Multi-Factor ExtensionsMartingalesThe Martingale Representation Theorem Changing Measures with Binomial Models Change of Measures under Brownian Filtration The Martingale Representation Theorem A Complete Market with Two Securities Replicating and Pricing of Contingent Claims Multi-Factor Extensions A Complete Market with Multiple Securities The Black–Scholes Formula NotesInterest Rates and Bonds Interest Rates and Fixed-Income Instruments Yields Zero-Coupon Bonds and Zero-Coupon Yields Forward Rates and Forward-Rate Agreements Yield-Based Bond Risk Management The Heath–Jarrow–Morton ModelLognormal Model: The Starting PointThe HJM ModelSpecial Cases of the HJM ModelEstimating the HJM Model from Yield Data A Case Study with a Two-Factor ModelMonte Carlo ImplementationsForward PricesForward MeasureBlack’s Formula for Call and Put Options Numeraires and Changes of MeasureNotesShort-Rate Models and Lattice ImplementationFrom Short-Rate Models to Forward-Rate Models General Markovian Models Binomial Trees of Interest Rates A General Tree-Building Procedure The LIBOR Market ModelLIBOR Market InstrumentsThe LIBOR Market ModelPricing of Caps and Floors Pricing of SwaptionsSpecifications of the LIBOR Market ModelMonte Carlo Simulation MethodCalibration of LIBOR Market ModelImplied Cap and Caplet Volatilities Calibrating the LIBOR Market Model to CapsCalibration to Caps, Swaptions, and Input Correlations Calibration MethodologiesSensitivity with Respect to the Input Prices NotesVolatility and Correlation AdjustmentsAdjustment due to CorrelationsAdjustment due to ConvexityTiming Adjustment Quanto Derivatives NotesAffine Term Structure ModelsAn Exposition with One-Factor ModelsAnalytical Solution of Riccarti Equations Pricing Options on Coupon Bonds Distributional Properties of Square-Root Processes Multi-Factor Models Swaption Pricing under ATSMsNotesReferences Index

"The book presents in a balanced way both theory and applications of interest rate modeling. …The book can serve as a textbook. It is self-contained in mathematics and presents rigorous justifications for almost all results. Many exercises are provided which often require computer implementation. To a large extent, this book can also serve as a research monograph as it contains many new results. The book shows the readers what has to be a competent quantitative analysis in financial markets."—Pavel Stoynov, Zentralblatt MATH 1173