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Mathematics of financial markets

Author: Elliott, Robert J. ; Kopp, P. Ekkehard Series: Springer finance Publisher: Springer, 2005.Edition: 2nd ed.Language: EnglishDescription: 352 p. ; 24 cm.ISBN: 0387212922Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print HG4515.3 .E55 2005
(Browse shelf)
001212061
Available 001212061
Total holds: 0

Includes bibliographical references and index

Digitized

Mathematics of Financial Market Contents Preface ..................................................................................................... v Preface to the Second Edition .......................................................................... vii 1 Pricing by Arbitrage 1 1.1 Introduction: Pricing and Hedging .................................................. 1 1.2 Single-Period Option Pricing Models .............................................. 10 1.3 A General Single-Period Model ................................................................ 12 1.4 A Single-Period Binomial Model ............................................................. 14 1.5 Multi-period Binomial Models.........................................................20 1.6 Bounds on Option Prices .......................................................................... 24 2 Martingale Measures 27 2.1 A General Discrete-Time Market Model ............................................... 27 2.2 Trading Strategies ........................................................................ 29 2.3 Martingales and Risk-Neutral Pricing .................................................. 35 2.4 Arbitrage Pricing: -Martingale Measures .............................................. 38 2.5 Strategies Using Contingent Claims...................................................... 43 2.6 Example: The Binomial Model ................................................................. 48 2.7 From CRR to Black-Scholes ..................................................................... 50 3 The First Fundamental Theorem 57 3.1 The Separating Hyperlane Theorem in W ............................................. 57 3.2 Construction of Martingale Measures 59 3.3 Pat hwise Description ................................................................................. 61 3.4 Examples ........................................................................................................ 69 3.5 General Discrete Models ........................................................................... 71 4 Complete Markets 87 4.1 Completeness and Martingale Representation .................................. 88 4.2 Completeness for Finite Market Models .............................................. 89 4.3 The CRR Model .............................................................................................. 91 4.4 The Splitting Index and Completeness ..................................................94 4.5 Incomplete Models: The Arbitrage Interval .......................................... 97 4.6 Characterisation of Complete Models 101 x CONTENTS 105 105 107 110 116 124 126 5 Discrete-time American Options 5.1 Hedging American Claims ............................................................ 5.2 Stopping Times and Stopped Processes ...................................... 5.3 Uniformly Integrable Martingales ................................................ 5.4 Optimal Stopping: The Snell Envelope......................................... 5.5 Pricing and Hedging American Options ...................................... 5.6 Consumption-Investment Strategies .......................................... 6 Continuous-Time Stochastic Calculus 131 6.1 Continuous-Time Processes ........................................................ 131 6.2 Martingales ................................................................................. 135 6.3 Stochastic Integrals................................................................... 141 6.4 The Ito Calculus ......................................................................... 149 6.5 Stochastic Differential Equations ............................................... 158 6.6 Markov Property of Solutions of SDEs ......................................... 162 7 Continuous-Time European Options 7.1 Dynamics ................................................................................... 7.2 Girsanov's Theorem ..................................................................... 7.3 Martingale Representation .......................................................... 7.4 Self-Financing Strategies ............................................................. 7.5 An Equivalent Martingale Measure ............................................. 7.6 Black-Scholes Prices ................................................................... 7.7 Pricing in a Multifactor Model ...................................................... 7.8 Barrier Options .......................................................................... 7.9 The Black-Scholes Equation ....................................................... 7.10 The Greeks ............................................................................... 167 167 168 174 183 185 193 198 204 214 217 8 The American Put Option 223 8.1 Extended Trading Strategies ....................................................... 223 8.2 Analysis of American Put Options ............................................... 226 8.3 The Perpetual Put Option ........................................................... 231 8.4 Early Exercise Premium .............................................................. 234 8.5 Relation to Free Boundary Problems ........................................... 238 8.6 An Approximate Solution ............................................................. 243 9 Bonds and Term Structure 9.1 Market Dynamics ........................................................................ 9.2 Future Price and Futures Contracts ......................................... 9.3 Changing Numéraire .................................................................. 9.4 A General Option Pricing Formula ............................................... 9.5 Term Structure Models ............................................................... 9.6 Short-rate Diffusion Models ........................................................ 9.7 The Heath-Jarrow-Morton Model ................................................ 9.8 A Markov Chain Model ................................................................. 247 247 252 255 258 262 264 277 282 CONTENTS xi 10 Consumption-Investment Strategies 285 10.1 Utility Functions ..................................................................... 285 10.2 Admissible Strategies ............................................................... 287 10.3 Maximising Utility of Consumption .......................................... 291 10.4 Maximisation of Terminal Utility ............................................... 296 10.5 Consumption and Terminal Wealth ......................................... 299 11 Measures of Risk 11.1 Value at Risk ........................................................................... 11.2 Coherent Risk Measures ......................................................... 11.3 Deviation Measures.................................................................. 11.4 Hedging Strategies with Shortfall Risk ..................................... Bibliography Index 303 304 308 316 320 329 349

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