An introduction to financial mathematics: option valuation
Gespeichert in:
| Vorheriger Titel: | Junghenn, Hugo D., 1939- Option valuation |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press, Taylor & Francis Group
[2019]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Chapman & Hall/CRC financial mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 303 Seiten Illustrationen |
| ISBN: | 9780367208820 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Preface 1 xi Basic Finance 1.1 *1.2 1.3 1.4 *1.5 1.6 Interest ......................................................................................... Inflation...................................................................................... Annuities................................................................................... Bonds......................................................................................... Internal Rate of Return .............................................................. Exercises ................................................................................... 2 Probability Spaces 2.1 2.2 2.3 2.4 2.5 2.6 Sample Spaces and Events ....................................................... Discrete Probability Spaces.................................................... General Probability Spaces ....................................................... Conditional Probability .......................................................... Independence............................................................................ Exercises ...................................................................................... 3 Random Variables 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 Introduction ............................................................................ General Properties of RandomVariables ................................ Discrete Random Variables .................................................... Continuous Random Variables .............................................. Joint Distributions of RandomVariables
............................. Independent Random Variables.............................................. Identically Distributed Random Variables............................ Sums of Independent RandomVariables................................ Exercises ...................................................................................... Options and Arbitrage 4.1 4.2 4.3 4.4 4.5 4.6 The Price Process of an Asset .............................................. Arbitrage................................................................................... Classification of Derivatives.................................................... Forwards .................................................................................. Currency Forwards................................................................... Futures ......................................................................................... 1 1 3 4 10 11 13 17 17 18 21 26 30 31 35 35 37 38 42 44 46 48 48 51 55 55 56 58 59 60 61 vii
Contents viii *4.7 4.8 4.9 4.10 4.11 *4.12 4.13 Equality of Forward and Future Prices................................. Call and Put Options .............................................................. Properties of Options ................................................................. Dividend-Paying Stocks........................................................... Exotic Options.......................................................................... Portfolios and Payoff Diagrams.............................................. Exercises .................................................................................. 63 64 67 69 70 73 76 5 Discrete-Time Portfolio Processes 5.1 Discrete Time Stochastic Processes ..................................... 5.2 Portfolio Processes and the Value Process............................ 5.3 Self-Financing Trading Strategies........................................... 5.4 Equivalent Characterizations of Self-Financing ................... 5.5 Option Valuation by Portfolios................................................. 5.6 Exercises ................................................................................... 79 79 83 84 85 87 88 6 Expectation 91 6.1 Expectation of a Discrete Random Variable............................ 91 6.2 Expectation of a Continuous Random Variable................... 93 6.3 Basic Properties of Expectation ........................................... 95 6.4 Variance of a Random Variable.............................................. 96 6.5 Moment Generating Functions
.............................................. 98 6.6 The Strong Law of Large Numbers........................................ 99 6.7 The Central Limit Theorem..................................................... 100 6.8 Exercises ................................................................................... 102 7 The Binomial Model 107 7.1 Construction of the Binomial Model...........................................107 7.2 Completeness and Arbitrage in the Binomial Model ............... Ill 7.3 Path-Independent Claims....................................................... 115 *7.4 Path-Dependent Claims.......................................................... 119 7.5 Exercises .........................................................................................121 8 Conditional Expectation 8.1 Definition of Conditional Expectation .................................. 8.2 Examples of Conditional Expectations.................................. 8.3 Properties of Conditional Expectation.................................. 8.4 Special Cases............................................................................ *8.5 Existence of Conditional Expectation ................................. 8.6 Exercises ................................................................................... 125 125 126 128 130 132 134 9 Martingales in Discrete Time Markets 135 9.1 Discrete Time Martingales .................................................... 135 9.2 The Value Process as a Martingale..............................................137 9.3 A Martingale View of the Binomial Model
......................... 138 9.4 The Fundamental Theorems of Asset Pricing ...................... 140
Contents *9.5 9.6 Change of Probability............................................................ Exercises ................................................................................. 10 American Claims in Discrete-Time Markets 10.1 10.2 10.3 10.4 10.5 10.6 10.7 Continuous-Time Stochastic Processes................................. Brownian Motion ................................................................... Stochastic Integrals ................................................................ The Ito-Doeblin Formula ....................................................... Stochastic Differential Equations.......................................... Exercises .................................................................................. 12 The Black-Scholes-Merton Model 12.1 12.2 12.3 12.4 *12.5 12.6 159 159 160 164 170 176 180 183 197 Continuous-Time Martingales...................................................... 197 Change of Probability and Girsanov’s Theorem........................ 201 Risk-Neutral Valuation of a Derivative................................. 204 Proofs of the Valuation Formulas.......................................... 205 Valuation under P .................................................................. 208 The Feynman-Kac Representation Theorem........................ 209 Exercises ........................................................................................211 14 Path-Independent Options 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 147 The Stock Price SDE ............................................................. 183
Continuous-Time Portfolios.................................................... 184 The Black-Scholes Formula .................................................... 185 Properties of the Black-Scholes Call Function..................... 188 The BS Formula as a Limit of CRR Formulas.......................... 191 Exercises .................................................................................. 194 13 Martingales in the Black-Scholes-Merton Model 13.1 13.2 13.3 13.4 *13.5 *13.6 13.7 142 144 Hedging an American Claim ...................................................... 147 Stopping Times ...................................................................... 149 Submartingales and Supermartingales ....................................... 151 Optimal Exercise of an American Claim.............................. 152 Hedging in the Binomial Model............................................. 154 Optimal Exercise in the Binomial Model ........................... 155 Exercises .................................................................................. 156 11 Stochastic Calculus 11.1 11.2 11.3 11.4 11.5 11.6 ix 213 Currency Options ................................................................... 213 Forward Start Options .......................................................... 216 Chooser Options...................................................................... 216 Compound Options ................................................................ 218 Quantos..................................................................................... 219 Options on
Dividend-Paying Stocks .......................................... 221 American Claims...................................................................... 224 Exercises .................................................................................. 226
x Contents 15 Path-Dependent Options 15.1 Barrier Options ....................................................................... 15.2 Lookback Options .................................................................... 15.3 Asian Options .......................................................................... 15.4 Other Options .......................................................................... 15.5 Exercises ................................................................................... 229 229 234 240 243 244 A Basic Combinatorics 249 В Solution of the BSM PDE 255 C Properties of the BSM Call Function 259 D Solutions to Odd-Numbered Problems 265 Bibliography 297 Index 299
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| id | DE-604.BV045867753 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:28:57Z |
| institution | BVB |
| isbn | 9780367208820 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031251104 |
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| physical | xiii, 303 Seiten Illustrationen |
| publishDate | 2019 |
| publishDateSearch | 2019 |
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| series2 | Chapman & Hall/CRC financial mathematics series |
| spelling | Junghenn, Hugo D. 1939- Verfasser (DE-588)1089835477 aut An introduction to financial mathematics option valuation Second edition Boca Raton CRC Press, Taylor & Francis Group [2019] xiii, 303 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Option (DE-588)4115452-6 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Option (DE-588)4115452-6 s Finanzmathematik (DE-588)4017195-4 s DE-604 Fortsetzung von Junghenn, Hugo D., 1939- Option valuation Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031251104&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Junghenn, Hugo D. 1939- An introduction to financial mathematics option valuation Option (DE-588)4115452-6 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4115452-6 (DE-588)4017195-4 |
| title | An introduction to financial mathematics option valuation |
| title_auth | An introduction to financial mathematics option valuation |
| title_exact_search | An introduction to financial mathematics option valuation |
| title_full | An introduction to financial mathematics option valuation |
| title_fullStr | An introduction to financial mathematics option valuation |
| title_full_unstemmed | An introduction to financial mathematics option valuation |
| title_old | Junghenn, Hugo D., 1939- Option valuation |
| title_short | An introduction to financial mathematics |
| title_sort | an introduction to financial mathematics option valuation |
| title_sub | option valuation |
| topic | Option (DE-588)4115452-6 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Option Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031251104&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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