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Interest Rate Modeling: Theory and Practice, Second Edition 2nd edition [Hardback]

(University of Science & Technology, Kowloon, Hong Kong)
  • Formāts: Hardback, 494 pages, height x width: 234x156 mm, weight: 852 g, 28 Tables, black and white; 96 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 25-Feb-2019
  • Izdevniecība: CRC Press Inc
  • ISBN-10: 0815378912
  • ISBN-13: 9780815378914
Citas grāmatas par šo tēmu:
Interest Rate Modeling: Theory and Practice, Second Edition 2nd editionPalielināt
  • Formāts: Hardback, 494 pages, height x width: 234x156 mm, weight: 852 g, 28 Tables, black and white; 96 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 25-Feb-2019
  • Izdevniecība: CRC Press Inc
  • ISBN-10: 0815378912
  • ISBN-13: 9780815378914
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780815378914.html
Keywords:
Containing many results that are new, or which exist only in recent research articles, Interest Rate Modeling: Theory and Practice, 2nd Edition portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods.

Features











Presents a complete cycle of model construction and applications, showing readers how to build and use models





Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments





Contains exercise sets and a number of examples, with many based on real market data





Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment





New to the 2nd edition: volatility smile modeling; a new paradigm for inflation derivatives modeling; an extended market model for credit derivatives; a dual-curved model for the post-crisis interest-rate derivatives markets; and an elegant framework for the xVA.
Preface to the First Edition xv
Preface to the Second Edition xix
Acknowledgments to the Second Edition xxi
Author xxiii
1 The Basics of Stochastic Calculus 1(22)
1.1 Brownian Motion
1(6)
1.1.1 Simple Random Walks
2(1)
1.1.2 Brownian Motion
3(3)
1.1.3 Adaptive and Non-Adaptive Functions
6(1)
1.2 Stochastic Integrals
7(4)
1.2.1 Evaluation of Stochastic Integrals
10(1)
1.3 Stochastic Differentials and Ito's Lemma
11(5)
1.4 Multi-Factor Extensions
16(3)
1.4.1 Multi-Factor Ito's Process
16(1)
1.4.2 Ito's Lemma
17(1)
1.4.3 Correlated Brownian Motions
17(1)
1.4.4 The Multi-Factor Lognormal Model
18(1)
1.5 Martingales
19(4)
2 The Martingale Representation Theorem 23(28)
2.1 Changing Measures with Binomial Models
23(6)
2.1.1 A Motivating Example
23(3)
2.1.2 Binomial Trees and Path Probabilities
26(3)
2.2 Change of Measures under Brownian Filtration
29(3)
2.2.1 The Radon-Nikodym Derivative of a Brownian Path
29(2)
2.2.2 The CMG Theorem
31(1)
2.3 The Martingale Representation Theorem
32(1)
2.4 A Complete Market with Two Securities
33(1)
2.5 Replicating and Pricing of Contingent Claims
34(2)
2.6 Multi-Factor Extensions
36(1)
2.7 A Complete Market with Multiple Securities
37(4)
2.7.1 Existence of a Martingale Measure
38(2)
2.7.2 Pricing Contingent Claims
40(1)
2.8 The Black-Scholes Formula
41(2)
2.9 Notes
43(8)
3 Interest Rates and Bonds 51(20)
3.1 Interest Rates and Fixed-Income Instruments
51(6)
3.1.1 Short Rate and Money Market Accounts
51(1)
3.1.2 Term Rates and Certificates of Deposit
52(1)
3.1.3 Bonds and Bond Markets
53(2)
3.1.4 Quotation and Interest Accrual
55(2)
3.2 Yields
57(4)
3.2.1 Yield to Maturity
57(2)
3.2.2 Par Bonds, Par Yields, and the Par Yield Curve
59(1)
3.2.3 Yield Curves for U.S. Treasuries
60(1)
3.3 Zero-Coupon Bonds and Zero-Coupon Yields
61(3)
3.3.1 Zero-Coupon Bonds
61(1)
3.3.2 Bootstrapping the Zero-Coupon Yields
62(3)
3.3.2.1 Future Value and Present Value
63(1)
3.4 Forward Rates and Forward-Rate Agreements
64(1)
3.5 Yield-Based Bond Risk Management
65(6)
3.5.1 Duration and Convexity
65(2)
3.5.2 Portfolio Risk Management
67(4)
4 The Heath-Jarrow-Morton Model 71(48)
4.1 Lognormal Model: The Starting Point
72(3)
4.2 The HJM Model
75(3)
4.3 Special Cases of the HJM Model
78(4)
4.3.1 The Ho-Lee Model
78(1)
4.3.2 The Hull-White (or Extended Vasicek) Model
79(3)
4.4 Estimating the HJM Model from Yield Data
82(10)
4.4.1 From a Yield Curve to a Forward-Rate Curve
82(5)
4.4.2 Principal Component Analysis
87(5)
4.5 A Case Study with a Two-Factor Model
92(1)
4.6 Monte Carlo Implementations
93(3)
4.7 Forward Prices
96(3)
4.8 Forward Measure
99(3)
4.9 Black's Formula for Call and Put Options
102(7)
4.9.1 Equity Options under the Hull-White Model
103(3)
4.9.2 Options on Coupon Bonds
106(3)
4.10 Numeraires and Changes of Measure
109(1)
4.11 Linear Gaussian Models
110(1)
4.12 Notes
111(8)
5 Short-Rate Models and Lattice Implementation 119(30)
5.1 From Short-Rate Models to Forward-Rate Models
120(2)
5.2 General Markovian Models
122(9)
5.2.1 One-Factor Models
128(2)
5.2.2 Monte Carlo Simulations for Options Pricing
130(1)
5.3 Binomial Trees of Interest Rates
131(7)
5.3.1 A Binomial Tree for the Ho-Lee Model
132(1)
5.3.2 Arrow-Debreu Prices
133(2)
5.3.3 A Calibrated Tree for the Ho-Lee Model
135(3)
5.4 A General Tree-Building Procedure
138(11)
5.4.1 A Truncated Tree for the Hull-White Model
139(5)
5.4.2 Trinomial Trees with Adaptive Time Steps
144(1)
5.4.3 The Black-Karasinski Model
145(4)
6 The LIBOR Market Model 149(40)
6.1 LIBOR Market Instruments
149(13)
6.1.1 LIBOR Rates
150(1)
6.1.2 Forward-Rate Agreements
150(2)
6.1.3 Repurchasing Agreement
152(1)
6.1.4 Eurodollar Futures
152(2)
6.1.5 Floating-Rate Notes
154(1)
6.1.6 Swaps
155(2)
6.1.7 Caps
157(1)
6.1.8 Swaptions
158(1)
6.1.9 Bermudan Swaptions
159(1)
6.1.10 LIBOR Exotics
160(2)
6.2 The LIBOR Market Model
162(5)
6.3 Pricing of Caps and Floors
167(1)
6.4 Pricing of Swaptions
168(7)
6.5 Specifications of the LIBOR Market Model
175(3)
6.6 Monte Carlo Simulation Method
178(7)
6.6.1 The Log-Euler Scheme
178(1)
6.6.2 Calculation of the Greeks
179(1)
6.6.3 Early Exercise
180(5)
6.7 Notes
185(4)
7 Calibration of LIBOR Market Model 189(36)
7.1 Implied Cap and Caplet Volatilities
190(2)
7.2 Calibrating the LIBOR Market Model to Caps
192(3)
7.3 Calibration to Caps, Swaptions, and Input Correlations
195(5)
7.4 Calibration Methodologies
200(23)
7.4.1 Rank-Reduction Algorithm
200(11)
7.4.2 The Eigenvalue Problem for Calibrating to Input Prices
211(12)
7.5 Sensitivity with Respect to the Input Prices
223(2)
8 Volatility and Correlation Adjustments 225(28)
8.1 Adjustment due to Correlations
226(8)
8.1.1 Futures Price versus Forward Price
226(4)
8.1.2 Convexity Adjustment for LIBOR Rates
230(2)
8.1.3 Convexity Adjustment under the Ho-Lee Model
232(1)
8.1.4 An Example of Arbitrage
232(2)
8.2 Adjustment due to Convexity
234(9)
8.2.1 Payment in Arrears versus Payment in Advance
235(1)
8.2.2 Geometric Explanation for Convexity Adjustment
236(1)
8.2.3 General Theory of Convexity Adjustment
237(4)
8.2.4 Convexity Adjustment for CMS and CMT Swaps
241(2)
8.3 Timing Adjustment
243(1)
8.4 Quanto Derivatives
244(5)
8.5 Notes
249(4)
9 Affine Term Structure Models 253(28)
9.1 An Exposition with One-Factor Models
254(7)
9.2 Analytical Solution of Riccarti Equations
261(4)
9.3 Pricing Options on Coupon Bonds
265(1)
9.4 Distributional Properties of Square-Root Processes
266(1)
9.5 Multi-Factor Models
266(6)
9.5.1 Admissible ATSMs
268(1)
9.5.2 Three-Factor ATSMs
269(3)
9.6 Swaption Pricing under ATSMs
272(6)
9.7 Notes
278(3)
10 Market Models with Stochastic Volatilities 281(34)
10.1 SABR Model
282(7)
10.2 The Wu and Zhang (2001) Model
289(4)
10.3 Pricing of Caplets
293(4)
10.4 Pricing of Swaptions
297(4)
10.5 Model Calibration
301(7)
10.6 Notes
308(7)
11 Levy Market Model 315(28)
11.1 Introduction to Levy Processes
315(8)
11.1.1 Infinite Divisibility
315(2)
11.1.2 Basic Examples of the Levy Processes
317(2)
11.1.2.1 Poisson Processes
317(1)
11.1.2.2 Compound Poisson Processes
317(1)
11.1.2.3 Linear Brownian Motion
318(1)
11.1.3 Introduction of the Jump Measure
319(1)
11.1.4 Characteristic Exponents for General Levy Processes
319(4)
11.2 The Levy HJM Model
323(5)
11.3 Market Model under Levy Processes
328(2)
11.4 Caplet Pricing
330(2)
11.5 Swaption Pricing
332(2)
11.6 Approximate Swaption Pricing via the Merton Formula
334(2)
11.7 Notes
336(7)
12 Market Model for Inflation Derivatives Modeling 343(20)
12.1 CPI Index and Inflation Derivatives Market
345(4)
12.1.1 TIPS
347(1)
12.1.2 ZCIIS
347(1)
12.1.3 YYIIS
348(1)
12.1.4 Inflation Caps and Floors
349(1)
12.1.5 Inflation Swaptions
349(1)
12.2 Rebuilt Market Model and the New Paradigm
349(7)
12.2.1 Inflation Discount Bonds and Inflation Forward Rates
349(2)
12.2.2 The Compatibility Condition
351(2)
12.2.3 Rebuilding the Market Model
353(1)
12.2.4 The New Paradigm
354(1)
12.2.5 Unifying the Jarrow-Yildirim Model
355(1)
12.3 Pricing Inflation Derivatives
356(4)
12.3.1 YYIIS
356(1)
12.3.2 Caps
357(1)
12.3.3 Swaptions
357(3)
12.4 Model Calibration
360(1)
12.5 Smile Modeling
361(1)
12.6 Notes
362(1)
13 Market Model for Credit Derivatives 363(30)
13.1 Pricing of Risky Bonds: A New Perspective
365(2)
13.2 Forward Spreads
367(2)
13.3 Two Kinds of Default Protection Swaps
369(2)
13.4 Par CDS Rates
371(2)
13.5 Implied Survival Curve and Recovery-Rate Curve
373(5)
13.6 Credit Default Swaptions and an Extended Market Model
378(6)
13.7 Pricing of CDO Tranches under the Market Model
384(7)
13.8 Notes
391(2)
14 Dual-Curve SABR-LMM Market Model for Post-Crisis Interest Rate Derivatives Markets 393(56)
14.1 LIBOR Market Model under Default Risks
395(6)
14.2 Swaps and Basis Swaps
401(2)
14.3 Option Pricing Using Heat Kernel Expansion
403(18)
14.3.1 Derivation of the Heat Kernel
405(6)
14.3.1.1 General Heat Kernel Expansion Formulae
405(2)
14.3.1.2 Heat Kernel Expansion for the Dual-Curve SABR-LMM Model
407(4)
14.3.2 Calculating the Volatility for Local Volatility Model
411(8)
14.3.2.1 Calculation of the Local Volatility Function
411(6)
14.3.2.2 Calculation of the Saddle Point
417(2)
14.3.3 Calculation of the Implied Black's Volatility
419(1)
14.3.4 Numerical Results for 3M Caplets
420(1)
14.4 Pricing 3M Swaptions
421(15)
14.4.1 Dynamics of the State Variables
421(6)
14.4.1.1 Swap Rate Dynamics under the Forward Swap Measure
425(2)
14.4.2 Geometric Inputs
427(2)
14.4.2.1 Inputs Parameter for the Heat Kernel Expansion
427(2)
14.4.3 Local Volatility Function of Swap Rates
429(1)
14.4.4 Calculation of the Saddle Point
430(2)
14.4.4.1 Interpolation in High Dimensional Cases
430(2)
14.4.5 Implied Black's Volatility
432(1)
14.4.6 Numerical Results for 3M Swaptions
432(4)
14.5 Pricing Caps and Swaptions of Other Tenors
436(6)
14.5.1 Linkage between 3M Rates and Rates of Other Tenors
436(3)
14.5.1.1 The 6M Risk-Free OIS Rates
436(1)
14.5.1.2 The 6M Expected Loss Rates
436(3)
14.5.2 Dynamics of the 6M Risky LIBOR Rates
439(1)
14.5.3 Dynamics of the 6M Swap Rates
440(2)
14.5.4 Numerical Results of 6M Caplets and Swaptions
442(1)
14.5.5 Model Calibration
442(1)
14.6 Notes
442(7)
15 xVA: Definition, Evaluation, and Risk Management 449(22)
15.1 Pricing through Bilateral Replications
453(6)
15.1.1 Margin Accounts, Collaterals, and Capitals
453(1)
15.1.2 Pricing in the Absence of Funding Cost
454(5)
15.2 The Rise of Other xVA
459(7)
15.3 Examples
466(2)
15.4 Notes
468(3)
References 471(18)
Index 489
Lixin Wu is a 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.