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Elementary Introduction To Stochastic Interest Rate Modeling, An [Kõva köide]

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This textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students.
Preface v
A Review of Stochastic Calculus
1(12)
Brownian Motion
1(1)
Stochastic Integration
2(6)
Quadratic Variation
8(2)
Ito's Formula
10(2)
Exercises
12(1)
A Review of Black-Scholes Pricing
13(16)
Call and Put Options
13(2)
Market Model and Portfolio
15(1)
PDE Method
16(2)
The Girsanov Theorem
18(2)
Martingale Method
20(6)
Exercises
26(3)
Short Term Interest Rate Models
29(4)
Mean-Reverting Models
29(1)
Constant Elasticity of Variance (CEV) Models
30(1)
Time-Dependent Models
30(1)
Exercises
31(2)
Pricing of Zero-Coupon Bonds
33(14)
Definition and Basic Properties
33(1)
Absence of Arbitrage and the Markov Property
34(2)
Absence of Arbitrage and the Martingale Property
36(1)
PDE Solution: Probabilistic Method
37(2)
PDE Solution: Analytical Method
39(1)
Numerical Simulations
40(3)
Exercises
43(4)
Forward Rate Modeling
47(10)
Forward Contracts
47(3)
Instantaneous Forward Rate
50(2)
Short Rates
52(1)
Parametrization of Forward Rates
53(1)
Curve Estimation
54(1)
Exercises
55(2)
The Heath-Jarrow-Morton (HJM) Model
57(16)
Restatement of Objectives
57(2)
Forward Vasicek Rates
59(5)
Spot Forward Rate Dynamics
64(1)
The HJM Condition
65(3)
Markov Property of Short Rates
68(2)
The Hull-White Model
70(1)
Exercises
71(2)
The Forward Measure and Derivative Pricing
73(12)
Forward Measure
73(3)
Dynamics under the Forward Measure
76(4)
Derivative Pricing
80(2)
Inverse Change of Measure
82(1)
Exercises
83(2)
Curve Fitting and a Two Factor Model
85(18)
Curve Fitting
85(3)
Deterministic Shifts
88(1)
The Correlation Problem
89(2)
Two-Factor Model
91(7)
Exercises
98(5)
Pricing of Caps and Swaptions on the LIBOR
103(18)
Pricing of Caplets and Caps
103(2)
Forward Rate Measure and Tenor Structure
105(2)
Swaps and Swaptions
107(1)
The London InterBank Offered Rates (LIBOR) Model
108(2)
Swap Rates on the LIBOR Market
110(2)
Swaption Pricing on the LIBOR Market
112(2)
Forward Swap Measures
114(4)
Exercises
118(3)
The Brace-Gatarek-Musiela (BGM) Model
121(14)
The BGM Model
121(3)
Cap Pricing
124(1)
Swaption Pricing
125(4)
Calibration of the BGM Model
129(3)
Exercises
132(3)
Appendix A: Mathematical Tools
135(8)
Appendix B: Some Recent Developments
143(4)
Solutions to the Exercises
147(26)
Bibliography 173(4)
Index 177