An introduction to quantitative finance:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2014
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| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 175 S. graph. Darst. |
| ISBN: | 9780199666591 9780199666584 |
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MARC
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Record in the Search Index
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| adam_text | Titel: An introduction to quantitative finance
Autor: Blyth, Stephen
Jahr: 2014
CONTENTS
PART I PRELIMINARIES
1 Preliminaries.......................................3
1.1 Interest rates and compounding 3
1.2 Zero coupon bonds and discounting 5
1.3 Annuities 6
1.4 Daycount conventions 7
1.5 An abridged guide to stocks, bonds and FX 8
1.6 Exercises 9
PART II FORWARDS, SWAPS AND OPTIONS
2 Forward contracts and forward prices......................13
2.1 Derivative contracts 13
2.2 Forward contracts 14
2.3 Forward on asset paying no income 14
2.4 Forward on asset paying known income 16
2.5 Review of assumptions 17
2.6 Value of forward contract 19
2.7 Forward on stock paying dividends and on currency 20
2.8 Physical versus cash settlement 20
2.9 Summary 21
2.10 Exercises 22
3 Forward rates and libor................................25
3.1 Forward zero coupon bond prices 25
3.2 Forward interest rates 26
3.3 Libor 27
3.4 Forward rate agreements and forward libor 27
3.5 Valuing floating and fixed cashflows 29
3.6 Exercises 30
4 Interest rate swaps...................................33
4.1 Swap definition 33
4.2 Forward swap rate and swap value 34
4.3 Spot-starting swaps 35
4.4 Swaps as difference between bonds 36
4.5 Exercises 37
5 Futures contracts....................................41
5.1 Futures definition 41
5.2 Futures versus forward prices 42
5.3 Futures on libor rates 43
5.4 Exercises 45
6 No-arbitrage principle................................47
6.1 Assumption of no-arbitrage 47
6.2 Monotonicity theorem 48
6.3 Arbitrage violations 49
6.4 Exercises 50
7 Options..........................................53
7.1 Option definitions 53
7.2 Put-call parity 56
7.3 Bounds on call prices 57
7.4 Call and put spreads 58
7.5 Butterflies and convexity of option prices 60
7.6 Digital options 61
7.7 Options on forward contracts 62
7.8 Exercises 64
PART III REPLICATION, RISK-NEUTRALITY
AND THE FUNDAMENTAL THEOREM
8 Replication and risk-neutrality on the binomial tree.............71
8.1 Hedging and replication in the two-state world 71
8.2 Risk-neutral probabilities 73
8.3 Multiple time steps 74
8.4 General no-arbitrage condition 76
8.5 Exercises 78
9 Martingales, numeraires and the fundamental theorem...........81
9.1 Definition of martingales 81
9.2 Numeraires and fundamental theorem 83
9.3 Change of numeraire on binomial tree 85
9.4 Fundamental theorem: a pragmatic example 86
9.5 Fundamental theorem: summary 87
9.6 Exercises 88
10 Continuous-time limit and Black-Scholes formula..............93
10.1 Lognormal limit 93
10.2 Risk-neutral limit 95
10.3 Black-Scholes formula 97
10.4 Properties of Black-Scholes formula 98
10.5 Delta and vega 101
10.6 Incorporating random interest rates 105
10.7 Exercises 106
11 Option price and probability duality......................Ill
11.1 Digitals and cumulative distribution function 111
11.2 Butterflies and risk-neutral density 113
11.3 Calls as spanning set 114
11.4 Implied volatility 115
11.5 Exercises 116
PART IV INTEREST RATE OPTIONS
12 Caps, floors and swaptions.............................119
12.1 Caplets 119
12.2 Caplet valuation and forward numeraire 120
12.3 Swaptions and swap numeraire 122
12.4 Summary 124
12.5 Exercises 124
13 Cancellable swaps and Bermudan swaptions.................127
13.1 European cancellable swaps 127
13.2 Callable bonds 128
13.3 Bermudan swaptions 130
13.4 Bermudan swaption exercise criteria 132
13.5 Bermudan cancellable swaps and callable bonds 134
13.6 Exercises 136
14 Libor-in-arrears and constant maturity swap contracts...........141
14.1 Libor-in-arrears 141
14.2 Libor-in-arrears convexity correction 142
14.3 Classic libor-in-arrears trade 144
14.4 Constant maturity swap contracts 145
14.5 Exercises 146
15 The Brace-Gatarek-Musiela framework....................149
15.1 B GM volatility surface 149
15.2 Option price dependence on BGM volatility surface 150
15.3 Exercises 153
PART V TOWARDS CONTINUOUS TIME
16 Rough guide to continuous time.........................157
16.1 Brownian motion as random walk limit 157
16.2 Stochastic differential equations and geometric Brownian motion 158
16.3 Ito s lemma 160
16.4 Black-Scholes equation 161
16.5 Ito and change of numeraire 162
Glossary of notation 167
References 171
Index 173
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| edition | 1. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:59:37Z |
| institution | BVB |
| isbn | 9780199666591 9780199666584 |
| language | English |
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| publishDate | 2014 |
| publishDateSearch | 2014 |
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| publisher | Oxford Univ. Press |
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| spelling | Blyth, Stephen Verfasser (DE-588)1047521784 aut An introduction to quantitative finance Stephen Blyth 1. ed. Oxford Oxford Univ. Press 2014 XVI, 175 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 s Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027002479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blyth, Stephen An introduction to quantitative finance Wirtschaftsmathematik (DE-588)4066472-7 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4135346-8 |
| title | An introduction to quantitative finance |
| title_auth | An introduction to quantitative finance |
| title_exact_search | An introduction to quantitative finance |
| title_full | An introduction to quantitative finance Stephen Blyth |
| title_fullStr | An introduction to quantitative finance Stephen Blyth |
| title_full_unstemmed | An introduction to quantitative finance Stephen Blyth |
| title_short | An introduction to quantitative finance |
| title_sort | an introduction to quantitative finance |
| topic | Wirtschaftsmathematik (DE-588)4066472-7 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| topic_facet | Wirtschaftsmathematik Optionspreistheorie |
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