An undergraduate introduction to financial mathematics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2012
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 464 S. graph. Darst. |
| ISBN: | 9789814407441 9812835350 |
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MARC
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| 245 | 1 | 0 | |a An undergraduate introduction to financial mathematics |c J. Robert Buchanan |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PREFACE VII
PREFACE TO THE SECOND EDITION IX
PREFACE TO THE FIRST EDITION XI
1. THE THEORY OF INTEREST . 1
1.1 SIMPLE INTEREST 1
1.2 COMPOUND INTEREST 3
1.3 CONTINUOUSLY COMPOUNDED INTEREST 4
1.4 PRESENT VALUE 6
1.5 TIME-VARYING INTEREST RATES 12
1.6 RATE OF RETURN / 14
1.7 CONTINUOUS INCOME STREAMS 15
1.8 EXERCISES . . 17
2. DISCRETE PROBABILITY 21
2.1 EVENTS AND PROBABILITIES 22
2.2 ADDITION RULE 23
2.3 CONDITIONAL PROBABILITY AND MULTIPLICATION RULE 24 2.4 RANDOM
VARIABLES AND PROBABILITY DISTRIBUTIONS 27 2.5 BINOMIAL RANDOM VARIABLES
28
2.6 EXPECTED VALUE 30
2.7 VARIANCE AND STANDARD DEVIATION 38
2.8 EXERCISES 42
IMAGE 2
XVI AN UNDERGRADUATE INTRODUCTION TO FINANCIAL MATHEMATICS
3. NORMAL RANDOM VARIABLES AND PROBABILITY 47
3.1 CONTINUOUS RANDOM VARIABLES 47
3.2 EXPECTED VALUE OF CONTINUOUS RANDOM VARIABLES 50 3.3 VARIANCE AND
STANDARD DEVIATION 54
3.4 NORMAL RANDOM VARIABLES 55
3.5 CENTRAL LIMIT THEOREM 64
3.6 LOGNORMAL RANDOM VARIABLES 66
3.7 PROPERTIES OF EXPECTED VALUE 70
3.8 PROPERTIES OF VARIANCE 73
3.9 EXERCISES 76
4. THE ARBITRAGE THEOREM 81
4.1 THE CONCEPT OF ARBITRAGE . 83
4.2 AN INTRODUCTION TO LINEAR PROGRAMMING 84
4.3 DUAL PROBLEMS 91
4.4 THE FUNDAMENTAL THEOREM OF FINANCE 103
4.5 EXERCISES 106
5. RANDOM WALKS AND BROWNIAN MOTION 111
5.1 INTUITIVE IDEA OF A RANDOM WALK I LL
5.2 DISCRETE RANDOM WALKS 112
5.3 FIRST STEP ANALYSIS 116
5.4 CONTINUOUS RANDOM WALKS 127
5.5 THE STOCHASTIC INTEGRAL 134
5.6 CONTINUOUS RANDOM WALKS WITH DRIFT 137
5.7 ITO PROCESSES 143
5.8 ITO S LEMMA 144
5.9 STOCK MARKET EXAMPLE 148
5.10 EXERCISES 150
6. FORWARDS AND FUTURES 155
6.1 DEFINITION OF A FORWARD CONTRACT 155
6*.2 PRICING A FORWARD CONTRACT 157
6.3 DIVIDENDS AND PRICING 162
6.4 INCORPORATING TRANSACTION COSTS 163
6.5 FUTURES 165
6.6 EXERCISES 168
IMAGE 3
CONTENTS XVII
7. OPTIONS 173
7.1 PROPERTIES OF OPTIONS 174
7.2 INCLUDING THE EFFECTS OF DIVIDENDS 178
7.3 PRICING AN OPTION USING A BINARY MODEL 180
7.4 BLACK-SCHOLES PARTIAL DIFFERENTIAL EQUATION 182
7.5 BOUNDARY AND INITIAL CONDITIONS 184
7.6 OPTION STRATEGIES 186
7.7 EXERCISES 194
8. SOLUTION OF THE BLACK-SCHOLES EQUATION 199
8.1 FOURIER TRANSFORMS 199
8.2 INVERSE FOURIER TRANSFORMS 202
8.3 CHANGING VARIABLES IN THE BLACK-SCHOLES PDE 203 8.4 SOLVING THE
BLACK-SCHOLES EQUATION 207
8.5 BINOMIAL MODEL (OPTIONAL) 211
8.6 EXERCISES 223
9. DERIVATIVES OF BLACK-SCHOLES OPTION PRICES 227
9.1 THETA 227
9.2 DELTA 229
9.3 GAMMA 231
9.4 VEGA 232
9.5 RHO 233
9.6 RELATIONSHIPS BETWEEN A, 9, AND T 235
9.7 EXERCISES 237
10. HEDGING 241
10.1 GENERAL PRINCIPLES 241
10.2 DELTA HEDGING 244
10.3 DELTA NEUTRAL PORTFOLIOS 249
10.4 GAMMA NEUTRAL PORTFOLIOS 250
10.5 EXERCISES 252
11. EXTENSIONS OF THE BLACK-SCHOLES MODEL 255
11.1 OPTIONS ON STOCKS PAYING CONTINUOUS DIVIDENDS 255 11.2 OPTIONS ON
STOCKS PAYING DISCRETE DIVIDENDS 260 11.3 EXERCISES 267
IMAGE 4
XVIII AN UNDERGRADUATE INTRODUCTION TO FINANCIAL MATHEMATICS
12. OPTIMIZING PORTFOLIOS 271
12.1 COVARIANCE AND CORRELATION 271
12.2 OPTIMAL PORTFOLIOS 279
12.3 UTILITY FUNCTIONS 282
12.4 EXPECTED UTILITY 288
12.5 PORTFOLIO SELECTION 290
12.6 MINIMUM VARIANCE ANALYSIS 294
12.7 MEAN-VARIANCE ANALYSIS 305
12.8 EXERCISES 310
13. AMERICAN OPTIONS 315
13.1 PARITY AND AMERICAN OPTIONS 315
13.2 AMERICAN PUTS VALUED BY A BINOMIAL MODEL 321
13.3 PROPERTIES OF THE BINOMIAL PRICING FORMULA 328
13.4 OPTIMAL EXERCISE TIME 331
13.5 EXERCISES 336
APPENDIX A SAMPLE STOCK MARKET DATA 339
APPENDIX B SOLUTIONS TO CHAPTER EXERCISES 343
B.I THE THEORY OF INTEREST 343
B.2 DISCRETE PROBABILITY 349
B.3 NORMAL RANDOM VARIABLES AND PROBABILITY 359
B.4 THE ARBITRAGE THEOREM 373
J3.5 RANDOM WALKS AND BROWNIAN MOTION 381
B.6 FORWARDS AND FUTURES T 394
B.7 OPTIONS 399
B.8 SOLUTION OF THE BLACK-SCHOLES EQUATION . 407
B.9 DERIVATIVES OF BLACK-SCHOLES OPTION PRICES 416
B.10 HEDGING 421
B.LL EXTENSIONS OF THE BLACK-SCHOLES MODEL 430
B.12 OPTIMIZING PORTFOLIOS 434
B.13 AMERICAN OPTIONS 445
BIBLIOGRAPHY 455
INDEX 459
|
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| dewey-sort | 3330.01 3513 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-10T00:27:01Z |
| institution | BVB |
| isbn | 9789814407441 9812835350 |
| language | English |
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| physical | XVIII, 464 S. graph. Darst. |
| publishDate | 2012 |
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| publisher | World Scientific |
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| spelling | Buchanan, J. Robert Verfasser (DE-588)102711332X aut An undergraduate introduction to financial mathematics J. Robert Buchanan 3. ed. Singapore [u.a.] World Scientific 2012 XVIII, 464 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finanzmathematik stw Business mathematics Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finanzmathematik (DE-588)4017195-4 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025427528&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buchanan, J. Robert An undergraduate introduction to financial mathematics Finanzmathematik stw Business mathematics Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4123623-3 |
| title | An undergraduate introduction to financial mathematics |
| title_auth | An undergraduate introduction to financial mathematics |
| title_exact_search | An undergraduate introduction to financial mathematics |
| title_full | An undergraduate introduction to financial mathematics J. Robert Buchanan |
| title_fullStr | An undergraduate introduction to financial mathematics J. Robert Buchanan |
| title_full_unstemmed | An undergraduate introduction to financial mathematics J. Robert Buchanan |
| title_short | An undergraduate introduction to financial mathematics |
| title_sort | an undergraduate introduction to financial mathematics |
| topic | Finanzmathematik stw Business mathematics Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik Business mathematics Lehrbuch |
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