Stochastic finance: an introduction with examples
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom
Cambridge University Press
2023
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | x, 252 Seiten Diagramme |
| ISBN: | 9781316511251 9781009048941 |
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Contents Preface Acknowledgements page ix x Part I Discrete-Time Models for Finance 1 Introduction to Finance 1.1 Motivation 1.2 Financial Markets 1.2.1 Primary Markets 1.2.2 Secondary Markets 1.2.3 Payoffs 1.2.4 Payoff Diagrams 1.3 Arbitrage Opportunities and Liquid Markets 1.4 Exercises 2 Discrete Probability 2.1 Basics 2.2 Conditional Expectation 2.2.1 Conditioning on an Event В 2.2.2 Conditioning on Partitions and Random Variables 2.2.3 Properties of Conditional Expectation 2.3 Modelling the Information Available in the Future 2.3.1 Motivation 2.3.2 Definition of a σ-Algebra 2.3.3 Visualisation of σ-Algebras 2.3.4 σ-Algebras Generated by RandomVariables 2.3.5 Measurable Random Variables andConditioning 2.4 Exercises 3 Binomial or CRR Model 3.1 Model Specification 3.2 Trading Strategies 3.3 Pricing of European Contingent Claims 3.3.1 One Period (T=l) 3 3 4 4 5 7 9 9 15 17 17 22 22 26 33 39 40 41 44 47 53 59 62 62 64 69 72 v
vi Contents 3.3.2 Multi-period Case (T Arbitrary) 3.4 American Contingent Claims 3.5 Exercises 4 Finite Market Model 4.1 Model Specification and Notation 4.1.1 Model Specification 4.1.2 Trading Strategies 4.1.3 Discounted Asset Prices 4.2 First Fundamental Theorem of Asset Pricing 4.3 Second Fundamental Theorem of Asset Pricing 4.4 Pricing of Replicable European Contingent Claims 4.5 Incomplete Markets 4.6 Exercises 5 Discrete Black-Scholes Model 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Heuristic Considerations on the Stock Price Model Specification Trading Strategies and Discounted Asset Prices Risk-Neutral Measure Black-Scholes Formula Replicating Strategies Exercises 80 93 95 97 97 97 98 99 100 108 113 116 120 123 123 125 126 128 131 133 135 Part II Continuous-Time Models for Finance 6 Continuous Probability Basics 6.1.1 General Probability Spaces 6.1.2 Measures on an Arbitrary Probability Space 6.1.3 Random Variables 6.1.4 Convergence of Random Variables 6.2 Review of Stochastic Processes 6.3 Filtrationsand Conditional Expectations 6.4 Exercises 6.1 7 Brownian Motion 7.1 Definition of Brownian Motion 7.2 Properties of Sample Paths of Brownian Motion 139 139 139 140 144 147 151 156 162 164 164 167
Contents 7.3 7.4 Transformations of Brownian Motion Exercises 8 Stochastic Integration 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 The Riemann Integral The Riemann-Stieltjes Integral Quadratic Variation Construction of the Stochastic Integral Properties of the Stochastic Integral Itô’s Formula Stochastic Differential Equations Exercises 9 The Black-Scholes Model 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Model Specification Trading Strategies Arbitrage and Risk-Neutral Measure Black-Scholes Formula The Black-Scholes Greeks 9.5.1 Volatility Terminal Value Claims Exercises Appendix A Supplementary Material A.l A.2 A.3 A.4 Elementary Limit Theorems Measures on Countable Sample Spaces Discontinuities of Cadlag Functions Omitted Proofs Bibliography Symbol Index Index vii 169 174 176 176 179 183 186 195 198 205 208 210 210 211 218 225 229 231 232 236 238 238 240 241 242 248 249 251 |
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| title | Stochastic finance an introduction with examples |
| title_auth | Stochastic finance an introduction with examples |
| title_exact_search | Stochastic finance an introduction with examples |
| title_exact_search_txtP | Stochastic finance an introduction with examples |
| title_full | Stochastic finance an introduction with examples Amanda Turner (University of Leeds), Dirk Zeindler (Lancester University) |
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| title_short | Stochastic finance |
| title_sort | stochastic finance an introduction with examples |
| title_sub | an introduction with examples |
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