Mathematics of finance: An intuitive introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2019]
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 144 Seiten Illustrationen |
| ISBN: | 9783030254421 |
Internformat
MARC
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| 300 | |a xvii, 144 Seiten |b Illustrationen | ||
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| 490 | 0 | |a Undergraduate texts in mathematics | |
| 650 | 4 | |a Quantitative Finance | |
| 650 | 4 | |a Game Theory, Economics, Social and Behav. Sciences | |
| 650 | 4 | |a Finance, general | |
| 650 | 4 | |a Macroeconomics/Monetary Economics//Financial Economics | |
| 650 | 4 | |a Finance | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Macroeconomics | |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804180681231695872 |
|---|---|
| adam_text | Contents 1 Preliminaries via Gambles.......................................................................... 1.1 A Football Game................................................................................... 1.1.1 Removing Uncertainty.............................................................. 1.1.2 Computations............................................................................ 1.1.3 Profit Curves............................................................................. 1.1.4 Fixed Income............................................................................. 1.1.5 Arbitrage......... ......................................................................... 1.1.6 Hedging Without Arbitrage..................................................... 1.1.7 A Cautionary Word of Interpretation...................................... 1.2 Expected Value and Variance................................................................ 1.2.1 Probability and PDF................................................................. 1.2.2 Random Variable....................................................................... 1.2.3 Expected Value.......................................................................... 1.2.4 Variance..................................................................................... 1.2.5 Standard Form......... ................................................................. 1.3 Fair Bets and Ensuring Profits....................................................... 1.3.1 Fair
Bet...................................................................................... 1.3.2 Making Money.......................................................................... 1.3.3 Horse Racing............................................................................. 1.4 Exercises................................................................................................. 1 1 2 3 4 4 5 6 7 9 9 14 14 15 18 18 19 20 21 24 2 Options........................................................................................................... 2.1 Calls....................................................................................................... 2.1.1 A Long Call............................................................................... 2.1.2 Going Short............................................................................... 2.1.3 Hedging..................................................................................... 2.2 Puts......................................................................................................... 2.2.1 A Long Put................................................................................. 2.2.2 Short Put.................................................................................... 2.2.3 Some Jargon .............................................................................. 29 29 30 33 34 35 35 37 37 XV
xvi Contents 2.3 Hedging................................................................................................... 2.3.1 Straddle........................... 2.3.2 Designing Portfolios.................................................................. 2.4 Put-Call Parity....................................................................................... 2.4.1 Present Value of Money...................................... 2.4.2 Security....................................................................................... 2.5 Information Gained.................................................. 2.5.1 Our Friend: Arbitrage................................................................ 2.5.2 Properties of Puts and Calls...................................................... 2.6 Exercises.................................................................................................. 38 38 39 42 43 44 47 48 49 50 3 Modeling......................................................................................................... 3.1 Assumptions and Modeling ............... 3.1.1 Taylor Series.............................................................................. 3.1.2 More Variables........................................................................... 3.1.3 Back to Modeling Approximations......................................... 3.2 Efficient Market Hypothesis.................................................................. 3.2.1 Modeling.................................................................................... 3.2.2 Random Variables
..................................................................... 3.2.3 Back to Finance......................................................................... 3.2.4 Random Effects......................................................................... 3.3 Interpretation.......................................................................................... 3.3.1 Probability Distribution ........................................................... 3.4 Exercises................................................................................................. 55 55 56 59 60 60 62 63 65 67 68 69 69 4 Some Probability........................................................................................... 4.1 Review of Some Probability................................................................. 4.1.1 Review of Chain Rule............................................................... 4.1.2 Finding New PDFs ................................................................... 4.2 Itô’s Lemma........................................................................................... 4.3 Application............................................................................................. 4.3.1 PDF for S(t)............................................................................... 4.3.2 Lognormal Distribution ............................................................ 4.4 Exercises................................................................................................. 71 71 74 76 77 79 81 82 84 5 The Black-Scholes Equation
....................................................................... 89 5.1 Black-Scholes Equation........................................................................ 90 5.2 Boundary Conditions............................................................................ 93 5.2.1 Heat Equation............................................................................ 93 5.2.2 Black-Scholes Boundary Conditions..................................... 94 5.3 Conversion to the Heat Equation.......................................................... 97 5.3.1 A Quick Tutorial in Differential Equations............................. 97 5.3.2 Eliminating the Variable Coefficients....................................... 101 5.4 Intuition................................................................................................... 102 5.5 Exercises............................................................................... 103
Contents xvii 6 Solutions of Black-Scholes.......................................................................... 105 6.1 The Heat Equation and Ce(S, t) Solution........................................... 105 6.2 Source of Ce(S, t) Terms.................................................................... 106 6.3 Interpretation......................................................................................... 107 6.4 Exercises................................................................................................. 109 7 Partial Information: The Greeks................................................................ 7.1 The Pe{S, t) Solution .......................................................................... 7.2 Here Come the Greeks !........................................................................ 7.2.1 The Hedge Ratio á Term .......................................................... 7.2.2 Changing 5; the Gamma Greek Г ......................................... 7.2.3 The Fake Greek—vega v.......................................................... 7.2.4 More Members of the Greek Party........................................... 7.3 Exercises................................................................................................. Ill Ill 112 112 116 117 118 120 8 Sketching and the AmericanOptions......................................................... 8.1 Using Sc and 8p to Sketch Ce(S, t) and Pe{S, t)............................. 8.1.1 Sketching CE(S,t) ................................................................... 8.1.2 Sketching
Pe(S, t) ................................................................... 8.1.3 Comparing Curves.................................................................... 8.2 Arbitrage and the American Option..................................................... 8.2.1 Simple Geometry for Puts........................................................ 8.2.2 Arbitrage with a Call................................................................ 8.2.3 New Rules; the American Option............................................ 8.3 Exercises..................................................................................... 121 121 121 123 124 124 125 126 129 130 9 Embellishments ............................................................................................ 9.1 Bonds..................................................................................................... 9.2 Dividends, or Other Embellishments.................................................... 9.2.1 A New Problem......................................................................... 9.2.2 Here Comes the Solution.......................................................... 9.3 Numerical Integration............................................................................ 9.3.1 The Heat Equation................................................................... 9.4 What Is Next?........................................................................................ 9.5 Exercises................................................................................................. 131 131 133 134 135 136 136 139 139
References............................................................................................................. 141 Index 143
|
| any_adam_object | 1 |
| author | Saari, Donald 1940- |
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| author_facet | Saari, Donald 1940- |
| author_role | aut |
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| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| spelling | Saari, Donald 1940- Verfasser (DE-588)124637418 aut Mathematics of finance An intuitive introduction Donald G. Saari Cham Springer [2019] © 2019 xvii, 144 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Finance, general Macroeconomics/Monetary Economics//Financial Economics Finance Mathematics Macroeconomics Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content (DE-588)4151278-9 Einführung gnd-content Finanzmathematik (DE-588)4017195-4 s b DE-604 Erscheint auch als Online-Ausgabe 978-3-030-25443-8 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=031631187&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saari, Donald 1940- Mathematics of finance An intuitive introduction Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Finance, general Macroeconomics/Monetary Economics//Financial Economics Finance Mathematics Macroeconomics Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4123623-3 (DE-588)4151278-9 |
| title | Mathematics of finance An intuitive introduction |
| title_auth | Mathematics of finance An intuitive introduction |
| title_exact_search | Mathematics of finance An intuitive introduction |
| title_full | Mathematics of finance An intuitive introduction Donald G. Saari |
| title_fullStr | Mathematics of finance An intuitive introduction Donald G. Saari |
| title_full_unstemmed | Mathematics of finance An intuitive introduction Donald G. Saari |
| title_short | Mathematics of finance |
| title_sort | mathematics of finance an intuitive introduction |
| title_sub | An intuitive introduction |
| topic | Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Finance, general Macroeconomics/Monetary Economics//Financial Economics Finance Mathematics Macroeconomics Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Finance, general Macroeconomics/Monetary Economics//Financial Economics Finance Mathematics Macroeconomics Finanzmathematik Lehrbuch Einführung |
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