| Description |
1 online resource (519 pages) |
| Series |
Chapman and Hall/CRC Financial Mathematics Ser |
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Chapman and Hall/CRC Financial Mathematics Ser
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| Contents |
Cover; Half Title; Series Page; Title Page; Copyright Page; Dediction; Contents; Preface to the First Edition; Preface to the Second Edition; Acknowledgments to the Second Edition; Author; 1. The Basics of Stochastic Calculus; 1.1 Brownian Motion; 1.1.1 Simple Random Walks; 1.1.2 Brownian Motion; 1.1.3 Adaptive and Non-Adaptive Functions; 1.2 Stochastic Integrals; 1.2.1 Evaluation of Stochastic Integrals; 1.3 Stochastic Differentials and Ito's Lemma; 1.4 Multi-Factor Extensions; 1.4.1 Multi-Factor Ito's Process; 1.4.2 Ito's Lemma; 1.4.3 Correlated Brownian Motions |
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1.4.4 The Multi-Factor Lognormal Model1.5 Martingales; 2. The Martingale Representation Theorem; 2.1 Changing Measures with Binomial Models; 2.1.1 A Motivating Example; 2.1.2 Binomial Trees and Path Probabilities; 2.2 Change of Measures under Brownian Filtration; 2.2.1 The Radon-Nikodym Derivative of a Brownian Path; 2.2.2 The CMG Theorem; 2.3 The Martingale Representation Theorem; 2.4 A Complete Market with Two Securities; 2.5 Replicating and Pricing of Contingent Claims; 2.6 Multi-Factor Extensions; 2.7 A Complete Market with Multiple Securities; 2.7.1 Existence of a Martingale Measure |
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2.7.2 Pricing Contingent Claims2.8 The Black-Scholes Formula; 2.9 Notes; 3. Interest Rates and Bonds; 3.1 Interest Rates and Fixed-Income Instruments; 3.1.1 Short Rate and Money Market Accounts; 3.1.2 Term Rates and Certificates of Deposit; 3.1.3 Bonds and Bond Markets; 3.1.4 Quotation and Interest Accrual; 3.2 Yields; 3.2.1 Yield to Maturity; 3.2.2 Par Bonds, Par Yields, and the Par Yield Curve; 3.2.3 Yield Curves for U.S. Treasuries; 3.3 Zero-Coupon Bonds and Zero-Coupon Yields; 3.3.1 Zero-Coupon Bonds; 3.3.2 Bootstrapping the Zero-Coupon Yields; 3.3.2.1 Future Value and Present Value |
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3.4 Forward Rates and Forward-Rate Agreements3.5 Yield-Based Bond Risk Management; 3.5.1 Duration and Convexity; 3.5.2 Portfolio Risk Management; 4. The Heath-Jarrow-Morton Model; 4.1 Lognormal Model: The Starting Point; 4.2 The HJM Model; 4.3 Special Cases of the HJM Model; 4.3.1 The Ho-Lee Model; 4.3.2 The Hull-White (or Extended Vasicek) Model; 4.4 Estimating the HJM Model from Yield Data; 4.4.1 From a Yield Curve to a Forward-Rate Curve; 4.4.2 Principal Component Analysis; 4.5 A Case Study with a Two-Factor Model; 4.6 Monte Carlo Implementations; 4.7 Forward Prices; 4.8 Forward Measure |
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4.9 Black's Formula for Call and Put Options4.9.1 Equity Options under the Hull-White Model; 4.9.2 Options on Coupon Bonds; 4.10 Numeraires and Changes of Measure; 4.11 Linear Gaussian Models; 4.12 Notes; 5. Short-Rate Models and Lattice Implementation; 5.1 From Short-Rate Models to Forward-Rate Models; 5.2 General Markovian Models; 5.2.1 One-Factor Models; 5.2.2 Monte Carlo Simulations for Options Pricing; 5.3 Binomial Trees of Interest Rates; 5.3.1 A Binomial Tree for the Ho-Lee Model; 5.3.2 Arrow-Debreu Prices; 5.3.3 A Calibrated Tree for the Ho-Lee Model |
| Notes |
5.4 A General Tree-Building Procedure |
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Print version record |
| Subject |
Interest rate futures -- Mathematical models
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Interest rates -- Mathematical models
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Interest rate futures -- Mathematical models
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Interest rates -- Mathematical models
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| Form |
Electronic book
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| ISBN |
9781351227414 |
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1351227416 |
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