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E-raamat: Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition)

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Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students.This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.
Preface vii
1 A Review of Stochastic Calculus
1(14)
1.1 Brownian Motion
1(1)
1.2 Stochastic Integration
2(6)
1.3 Quadratic Variation
8(2)
1.4 Ito's Formula
10(2)
1.5 Exercises
12(3)
2 A Review of Black-Scholes Pricing and Hedging
15(18)
2.1 Call and Put Options
15(2)
2.2 Market Model and Portfolio
17(1)
2.3 PDE Method
18(2)
2.4 The Girsanov Theorem
20(3)
2.5 Martingale Method
23(7)
2.6 Exercises
30(3)
3 Short Term Interest Rate Models
33(6)
3.1 Mean-Reverting Models
33(1)
3.2 Constant Elasticity of Variance (CEV) Models
34(1)
3.3 Time-Dependent Models
35(1)
3.4 Exercises
35(4)
4 Pricing of Zero-Coupon Bonds
39(16)
4.1 Definition and Basic Properties
39(1)
4.2 Absence of Arbitrage and the Markov Property
40(2)
4.3 Absence of Arbitrage and the Martingale Property
42(2)
4.4 PDE Solution: Probabilistic Method
44(2)
4.5 PDE Solution: Analytical Method
46(1)
4.6 Numerical Simulations
47(3)
4.7 Exercises
50(5)
5 Forward Rate Modeling
55(10)
5.1 Forward Contracts
55(3)
5.2 Instantaneous Forward Rate
58(2)
5.3 Short Rates
60(1)
5.4 Parametrization of Forward Rates
61(1)
5.5 Curve Estimation
62(1)
5.6 Exercises
63(2)
6 The Heath-Jarrow-Morton (HJM) Model
65(16)
6.1 Restatement of Objectives
65(2)
6.2 Forward Vasicek Rates
67(5)
6.3 Spot Forward Rate Dynamics
72(1)
6.4 The HJM Condition
73(3)
6.5 Markov Property of Short Rates
76(2)
6.6 The Hull-White Model
78(1)
6.7 Exercises
79(2)
7 The Forward Measure and Derivative Pricing
81(16)
7.1 Forward Measure
81(4)
7.2 Dynamics under the Forward Measure
85(3)
7.3 Derivative Pricing
88(4)
7.4 Inverse Change of Measure
92(1)
7.5 Exercises
93(4)
8 Curve Fitting and a Two-Factor Model
97(18)
8.1 Curve Fitting
97(3)
8.2 Deterministic Shifts
100(1)
8.3 The Correlation Problem
101(3)
8.4 Two-Factor Model
104(7)
8.5 Exercises
111(4)
9 A Credit Default Model
115(10)
9.1 Survival Probabilities
115(2)
9.2 Stochastic Default
117(2)
9.3 Defaultable Bonds
119(1)
9.4 Credit Default Swaps
120(2)
9.5 Exercises
122(3)
10 Pricing of Caps and Swaptions on the LIBOR
125(24)
10.1 Pricing of Caplets and Caps
125(2)
10.2 Forward Rate Measure and Tenor Structure
127(4)
10.3 Swaps and Swaptions
131(2)
10.4 The London InterBank Offered Rates (LIBOR) Model
133(1)
10.5 Swap Rates on the LIBOR Market
134(3)
10.6 Forward Swap Measures
137(5)
10.7 Swaption Pricing on the LIBOR Market
142(1)
10.8 Exercises
143(6)
11 The Brace-Gatarek-Musiela (BGM) Model
149(14)
11.1 The BGM Model
149(3)
11.2 Cap Pricing
152(1)
11.3 Swaption Pricing
153(4)
11.4 Calibration of the BGM Model
157(3)
11.5 Exercises
160(3)
12 Appendix A: Mathematical Tools
163(8)
13 Appendix B: Some Recent Developments
171(4)
14 Solutions to the Exercises
175(46)
Bibliography 221(4)
Index 225(2)
Author Index 227
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