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Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition) [Kõva köide]

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This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations. The types of interest rates considered range from short rates to forward rates such as LIBOR and swap rates, which are presented in the HJM and BGM frameworks. The pricing and hedging of interest rate and fixed income derivatives such as bond options, caps, and swaptions, are treated using forward measure techniques. An introduction to default bond pricing and an outlook on model calibration are also included as additional topics. This third edition represents a significant update on the second edition published by World Scientific in 2012. Most chapters have been reorganized and largely rewritten with additional details and supplementary solved exercises. New graphs and simulations based on market data have been included, together with the corresponding R codes. The approach chosen is based on a step-by-step presentation of concepts, with a focus on explicit calculations. This new edition also contains 75 exercises and 4 problems with detailed solutions, making it suitable for advanced undergraduate and graduate level students.

Preface v
Introduction vii
List of Figures
xv
List of Tables
xvii
1 A Review of Stochastic Calculus
1(20)
1.1 Brownian Motion
1(2)
1.2 Stochastic Integration
3(5)
1.3 Definite Stochastic Integral
8(2)
1.4 Quadratic Variation
10(3)
1.5 Ito's Formula
13(3)
Exercises
16(5)
2 A Review of Black-Scholes Pricing and Hedging
21(18)
2.1 Call and Put Options
21(2)
2.2 Market Model and Self-Financing Portfolio
23(1)
2.3 PDE Method
24(1)
2.4 The Girsanov Theorem
25(5)
2.5 Martingale Method
30(7)
Exercises
37(2)
3 Short-Term Interest Rate Models
39(16)
3.1 Mean-Reverting Models
39(5)
3.2 Constant Elasticity of Variance (CEV) Models
44(1)
3.3 Time-Dependent Affine Models
45(1)
3.4 Calibration of the Vasicek Model
45(2)
3.5 Time Series Modeling
47(3)
Exercises
50(5)
4 Pricing of Zero-Coupon and Coupon Bonds
55(20)
4.1 Definition and Basic Properties
55(4)
4.2 Bond Pricing PDE
59(3)
4.3 Probabilistic Solution
62(5)
4.4 Numerical Simulations
67(2)
4.5 Bond Prices and Yield Data
69(1)
Exercises
70(5)
5 Forward Rates and Swap Rates
75(22)
5.1 Forward Rates
75(2)
5.2 Instantaneous Forward Rates
77(6)
5.3 LIBOR Rates
83(3)
5.4 Swap Rates
86(4)
5.5 Yield Curve Data
90(2)
Exercises
92(5)
6 Curve Fitting and a Two-Factor Model
97(22)
6.1 Parametrization of Forward Rates
97(5)
6.2 Fitting Curve Models to Market Data
102(2)
6.3 Deterministic Shifts
104(1)
6.4 The Correlation Problem
105(2)
6.5 Two-Factor Model
107(8)
Exercises
115(4)
7 Forward Rate Modeling
119(18)
7.1 The HJM Model
119(2)
7.2 Absence of Arbitrage
121(4)
7.3 HJM-Vasicek Forward Rates
125(3)
7.4 Markov Property of Short Rates
128(4)
7.5 The BGM Model
132(3)
Exercises
135(2)
8 Forward Measures and Derivative Pricing
137(38)
8.1 Forward Rate Measures
137(7)
8.2 Dynamics under the Forward Measure
144(5)
8.3 Bond Options
149(3)
8.4 Vasicek Bond Option Pricing
152(3)
8.5 Forward Swap Measures
155(8)
Exercises
163(12)
9 Pricing of Caps and Swaptions
175(38)
9.1 Black Caplet Pricing
175(6)
9.2 Swaps and Swaptions
181(4)
9.3 Black Swaption Pricing
185(3)
9.4 Swaption Pricing in the BGM Model
188(5)
9.5 Calibration of the BGM Model
193(3)
Exercises
196(17)
10 Default Bond Pricing
213(18)
10.1 Survival Probabilities
213(2)
10.2 Stochastic Default
215(3)
10.3 Defaultable Bonds
218(2)
10.4 Estimating Default Rates
220(2)
10.5 Credit Default Swaps
222(3)
Exercises
225(6)
11 Appendix: Mathematical Tools
231(8)
12 Solutions to the Exercises
239(104)
Bibliography 343(4)
Index 347(6)
Author Index 353