Financial mathematics: a comprehensive treatment in discrete time
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
2021
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Chapman & Hall/CRC financial mathematics series
A Chapman & Hall book |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032796334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverzeichnis Seite 795 - 798. - Literaturangaben |
| Umfang: | xxii, 567 Seiten Illustrationen, Diagramme |
| ISBN: | 9781138587878 9781032023076 |
Internformat
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| 245 | 1 | 0 | |a Financial mathematics |b a comprehensive treatment in discrete time |c by Giuseppe Campolieti (Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario), Roman N. Makarov (Associate Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario) |
| 250 | |a Second edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2021 | |
| 300 | |a xxii, 567 Seiten |b Illustrationen, Diagramme | ||
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| 490 | 0 | |a Chapman & Hall/CRC financial mathematics series | |
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Datensatz im Suchindex
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Contents List of Figures xjjj List of Tables xvii Preface xix I Introduction to Pricing and Management of Financial Secu rities 1 Mathematics of Compounding 1.1 Interest and Return . 1.1.1 Amount Function and Return. 1.1.2 Simple Interest. 1.1.3 Periodic Compound Interest. 1.1.4 Continuous Compound Interest. 1.1.5 Equivalent Rates. 1.1.6 Continuously Varying Interest Rates. 1.2 Time Value of Moneyand Cash Flows. 1.2.1 Equations of Value. 1.2.2 Deterministic Cash Flows and Their Net Present Values. 1.3 Annuities. 1.3.1 Simple Annuities. 1.3.2 Determining the Term of an Annuity. 1.3.3 General Annuities.
1.3.4 Perpetuities. 1.3.5 Continuous Annuities . 1.4 Bonds. 1.4.1 Introduction and Terminology. 1.4.2 Zero-Coupon Bonds. 1.4.3 Coupon Bonds. 1.4.4 Serial Bonds, Strip Bonds, and Callable Bonds. 1.5 Yield Rates. 1.5.1 Internal Rate of Return and Evaluation Criteria. 1.5.2 Determining Yield Rates for Bonds. 1.5.3 Approximation Methods. 1.5.4 The Yield Curve. 1.6 Yield Risk and Duration . 1.6.1 Immunization. 1.7 Exercises
. 1 3 3 3 6 7 10 11 14 16 16 18 21 21 26 27 28 29 31 31 31 33 34 36 36 38 40 47 51 55 57 vii
Contents 2 Primer on Pricing Risky Securities 2.1 Stocks and Stock Price Models. 2.1.1 Underlying Assets and Derivative Securities. 2.1.2 Basic Assumptions for Asset Price Models. 2.2 Basic Price Models . 2.2.1 A Single-Period Binomial Model. 2.2.2 A Discrete-Time Model with a Finite Number of States. 2.2.3 Introducing the Binomial Tree Model . 2.2.4 Recursive Construction of a Binomial Tree . 2.2.5 Self-Financing Investment Strategies in the Binomial Model. 2.2.6 Log-Normal PricingModel . 2.3 Arbitrage and Risk-Neutral Pricing . 2.3.1 The Law of One Price. 2.3.2 A First Look at Arbitrage in the Single-PeriodBinomial Model . 2.3.3 Arbitrage in the Binomial Tree Model. 2.3.4 Risk-Neutral Probabilities. 2.3.5 Martingale
Property. 2.3.6 Risk-Neutral Log-Normal Model. 2.4 Value at Risk. 2.5 Dividend Paying Stock . 2.6 Exercises . 65 65 65 66 67 67 74 77 82 83 86 91 92 93 95 96 98 99 100 103 106 3 Portfolio Management 113 3.1 Expected Utility Functions . 113 3.1.1 Utility Functions. 113 3.1.2 Mean-Variance Criterion. 121 3.2 Portfolio Optimization forTwo Assets. 122 3.2.1 Portfolio of Two Risky Assets. 122 3.2.2 Portfolio Lines. 126 3.2.3 The Minimum Variance Portfolio. 129 3.2.4 Selection of Optimal Portfolios. 131 3.3 Portfolio Optimization forN
Assets. 137 3.3.1 Portfolios of Several Assets. 137 3.3.2 The Minimum Variance Portfolio. 140 3.3.3 Minimum Variance Portfolio Line. 141 3.3.4 Case without Short Selling . 144 3.3.5 Maximum Expected Utility Portfolio. 145 3.3.6 Efficient Frontier and Capital Market Line. 147 3.4 The Capital Asset Pricing Model. 152 3.5 Exercises . 154 4 Primer on Derivative Securities 163 4.1 Forward Contracts. 163 4.1.1 No-Arbitrage Evaluation of Forward Contracts. 165 4.1.2 Value of a Forward Contract . 170 4.2 Basic Options Theory . 171 4.2.1 Payoffs of Standard Options. 172 4.2.2 Put-Call
Parities. 175 4.2.3 Properties of European Options. 176 4.2.4 Early Exercise and American Options. 178 4.2.5 Nonstandard Егігореап-Style Options. ISO
Contents 4.3 4.4 II Fundamentals of Option Pricing . 4.3.1 Pricing of European-Styíe Derivatives in the Binomial Tree Model . 183 183 4.3.2 4.3.3 191 Pricing of American Options in the Binomial Tree Model. Option Pricing in the Log-Normal Model: The Black- Schoies-Merton Formula. 4.3.4 Greeks and Hedging of Options. 4.3.5 Black- Scholes Equation. Exercises . Discrete-Time Modelling 192 196 202 206 217 5 Single-Period Arrow-Debreu Models 219 5.1 Specification of the Model . 219 5.1.1 Finite-State Economy. Vector Space of Payoffs. Securities. 219 5.1.2 Initial Price Vector and Payoff Matrix. 222 5.1.3 Portfolios of Base Securities. 223 5.2 Analysis of the Arrow-Debreu Model . 224 5.2.1 Redundant Assets and Attainable Securities. 224 5.2.2 Completeness of
the Model. 227 5.3 No-Arbitrage Asset Pricing. 229 5.3.1 The Law of One Price. 229 5.3.2 Arbitrage. 231 5.3.3 The First Fundamental Theorem of Asset Pricing. 232 5.3.4 Risk-Neutral Probabilities. 236 5.3.5 The Second Fundamental Theorem of Asset Pricing . 239 5.3.6 Investment Portfolio Optimization. 240 5.4 Pricing in an Incomplete Market. 243 5.4.1 A Trinomial Model of an Incomplete Market . 243 5.4.2 Pricing Unattainable Payoffs: The Bid-Ask Spread. 246 5.5 Change of Numéraire . 252 5.5.1 The Concept of a Numéraire Asset. 252 5.5.2 Change of Numeraire in a Binomial Model. 253 5.5.3 Change of Numéraire in a General Single Period Model. 254 5.6
Exercises . 261 6 Introduction to Discrete-Time Stochastic Calculus 271 6.1 A Multi-Period Binomial Probability Model . 271 6.1.1 The Binomial Probability Space . 271 6.1.2 Random Processes. 277 6.2 Information Flow . 280 6.2.1 Partitions and Their Refinements. 280 6.2.2 Sigma-Algebras. 284 6.2.3 Filtration. 290 6.2.4 Filtered Probability Space. 292 6.3 Conditional Expectation and Martingales. 293 6.3.1 Measurability of Random Variables and Processes . 293 6.3.2 Conditional Expectations. 295 6.3.3 Properties of Conditional Expectations. 301 6.3.4 Conditioning in the
Binomial Model. 305 6.3.5 Binomial Model with Interdependent Market Moves. 308 6.3.6 Sub-. Super-, and True Martingales. 312
Contents 6.3.7 Classification of Stochastic Processes. 315 6.3.8 Stopping Times. 317 6.4 Exercises . 324 7 Replication and Pricing in the Binomial Tree Model 7.1 The Standard Binomial Tree Model . 7.2 Self-Financing Strategies and Their Value Processes . 7.2.1 Equivalent Martingale Measures for the Binomial Model. 7.3 Dynamic Replication in the Binomial Tree Model . 7.3.1 Dynamic Replication of Payoffs. 7.3.2 Replication and Valuation of Random Cash Flows. 7.4 Pricing and Hedging Non-Path-Dependent Derivatives. 7.5 Pricing Formulae for Standard European Options . 7.6 Pricing and Hedging Path-Dependent Derivatives . 7.6.1 Average Asset Prices and Asian Options: Recursive Evaluation . . . 7.6.2 Extreme Asset Prices and Lookback Options. 7.6.3 Recursive Evaluation of Lookback Options . 7.7 American Options. 7.7.1
Writer’s Perspective·. Pricing arid Hedging. 7.7.2 Buyer’s Perspective: Optima! Exercise. 7.7.3 Early-Exercise Boundary for Non-Path-Dependent Options. 7.7.4 Pricing American Options: The Case with Dividends. 7.8 Exercises . 33I 331 334 338 341 341 350 351 356 361 361 365 366 371 371 378 386 387 391 8 General Multi-Asset Multi-Period Model 8.1 Main Elements of the Model . 8.2 Assets, Portfolios, and Strategies. 8.2.1 Payoffs and Assets. 8.2.2 Static and Dynamic Portfolios . 8.2.3 Self-Financing Strategies. 8.2.4 Replication of Payoffs. 8.3 Fundamental Theorems of Asset Pricing. 8.3.1 Arbitrage Strategies. 8.3.2 Enhancing the Law of One Price. 8.3.3 Equivalent Martingale Measures
. 8.3.4 Calculation of Martingale Measures . 8.3.5 The First and Second FTAP . 8.3.6 Pricing and Hedging Derivatives. 8.3.7 Pricing under the Markov Property. 8.3.8 Radofl-Nikodym Derivative Process and Change of Numeraire . . . 8.4 More Examples of Discrete-Time Models . 8.4.1 Binomial Tree Model with Stochastic Volatility. 8.4.2 Binomial Tree Model for Interest Rates. 8.4.3 Interest Rates with the Markov Property . 8.4.4 Forward Measures for Interest-Rate Derivative Pricing. 8.5 Exercises . 397 397 400 400 403 403 405 406 406 407 408 410 413 415 416 422 433 433 436 443 448 458
Contents A Elementary Probability Theory A.l Probability Space . A.1.1 A Sample Space and Events. A.l.2 Probability. A.1.3 Probability Space. A.1.4 Counting Techniques and CombinatorialProbabilities. A.1.5 Conditional Probability. A.1.6 Law of Total Probability and Bayes’Formula. A.l.7 Independence of Events. A.2 Univariate Probability Distributions. A.2.1 Random Variables. A.2.2 Cumulative Distribution Function . A.2.3 Discrete Probability Distributions . A.2.4 Continuous Probability Distributions. A.3 Mathematical Expectations and Other Moments . A.3.1 Mathematical Expectation of a DiscreteRandom Variable. A.3.2 Variance and Other Moments.
A.3.3 Mean, Variance, and Median of a Continuous Random Variable . . . A.3.4 Moment Generating Functions. A.4 Discrete and Continuous Probability Distributions. A.4.1 Bernoulli Trials. A.4.2 Bernoulli Distribution. A.4.3 Binomial Distribution. A.4.4 Hypergeometric Distribution. A.4.5 Geometric Distribution . A.4.6 Negative Binomial Distribution. A.4.7 Poisson Distribution. A.4.8 Continuous Uniform Distribution. A.4.9 Exponential Distribution . A.4.10 Normal Distribution. A.4.11 Gamma Distribution. A.4.12 Transformation of Continuous Random Variables. A.5 A Joint Probability Distribution . A.5.1 Bivariate Continuous
Probability Distributions. A.5.2 Independence of Random Variables. A.6 Limit Theorems . A.6.1 Chebyshev’s Theorem. A.6.2 Sum of Random Variables. A.6.3 Sample Mean and Limit Theorems. A.6.4 The Law of Large Numbers. 463 463 463 467 470 471 475 477 479 481 481 483 484 487 491 491 494 496 498 500 500 501 502 504 505 506 507 508 508 510 514 515 516 519 520 523 523 524 525 526 В Answers and Hints to Exercises 529 B.l Chapter 1. 529 B.2 Chapter 2. 531 B.3 Chapter 3. -533 B.4 Chapter 4. 534 B.5 Chapter 5. 537 B.6 Chapter
6. 542 B.7 Chapter 7. 546 B.8 Chapter 8. 550
xii C Glossary ofSymbols and Abbreviations Contents 553 D Greek Alphabet 557 References 55g Index 503 |
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| indexdate | 2025-01-30T17:03:23Z |
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| spelling | Campolieti, Giuseppe Verfasser (DE-588)1241207194 aut Financial mathematics a comprehensive treatment in discrete time by Giuseppe Campolieti (Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario), Roman N. Makarov (Associate Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario) Second edition Boca Raton ; London ; New York CRC Press 2021 xxii, 567 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series A Chapman & Hall book Literaturverzeichnis Seite 795 - 798. - Literaturangaben Finanzmathematik (DE-588)4017195-4 gnd rswk-swf aFinancexMathematical models Finanzmathematik (DE-588)4017195-4 s DE-604 Makarov, Roman Verfasser (DE-588)1038679419 aut Erscheint auch als Online-Ausgabe 978-0-429-50366-5 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=032796334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4017195-4 |
| title | Financial mathematics a comprehensive treatment in discrete time |
| title_auth | Financial mathematics a comprehensive treatment in discrete time |
| title_exact_search | Financial mathematics a comprehensive treatment in discrete time |
| title_full | Financial mathematics a comprehensive treatment in discrete time by Giuseppe Campolieti (Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario), Roman N. Makarov (Associate Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario) |
| title_fullStr | Financial mathematics a comprehensive treatment in discrete time by Giuseppe Campolieti (Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario), Roman N. Makarov (Associate Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario) |
| title_full_unstemmed | Financial mathematics a comprehensive treatment in discrete time by Giuseppe Campolieti (Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario), Roman N. Makarov (Associate Professor, Department of Mathematics, Wilfried Laurier University, Waterloo, Ontario) |
| title_short | Financial mathematics |
| title_sort | financial mathematics a comprehensive treatment in discrete time |
| title_sub | a comprehensive treatment in discrete time |
| topic | Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik |
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