An elementary introduction to mathematical finance:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Cover image Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Physical Description: | XV, 305 S. graph. Darst. |
| ISBN: | 9780521192538 |
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| adam_text | Titel: An elementary introduction to mathematical finance
Autor: Ross, Sheldon M.
Jahr: 2011
Contents
Introduction and Preface page xi
1 Probability 1
1.1 Probabilities and Events 1
1.2 Conditional Probability 5
1.3 Random Variables and Expected Values 9
1.4 Co variance and Correlation 14
1.5 Conditional Expectation 16
1.6 Exercises 17
2 Normal Random Variables 22
2.1 Continuous Random Variables 22
2.2 Normal Random Variables 22
2.3 Properties of Normal Random Variables 26
2.4 The Central Limit Theorem 29
2.5 Exercises 31
3 Brownian Motion and Geometric Brownian Motion 34
3.1 Brownian Motion 34
3.2 Brownian Motion as a Limit of Simpler Models 35
3.3 Geometric Brownian Motion 38
3.3.1 Geometric Brownian Motion as a Limit
of Simpler Models 40
3.4 *The Maximum Variable 40
3.5 The Cameron-Martin Theorem 45
3.6 Exercises 46
4 Interest Rates and Present Value Analysis 48
4.1 Interest Rates 48
4.2 Present Value Analysis 52
4.3 Rate of Return 62
4.4 Continuously Varying Interest Rates 65
4.5 Exercises 67
viii Contents
5 Pricing Contracts via Arbitrage 73
5.1 An Example in Options Pricing 73
5.2 Other Examples of Pricing via Arbitrage 77
5.3 Exercises 86
6 The Arbitrage Theorem 92
6.1 The Arbitrage Theorem 92
6.2 The Multiperiod Binomial Model 96
6.3 Proof of the Arbitrage Theorem 98
6.4 Exercises 102
7 The Black-Scholes Formula 106
7.1 Introduction 106
7.2 The Black-Scholes Formula 106
7.3 Properties of the Black-Scholes Option Cost 110
7.4 The Delta Hedging Arbitrage Strategy 113
7.5 Some Derivations 118
7.5.1 The Black-Scholes Formula 119
7.5.2 The Partial Derivatives 121
7.6 European Put Options 126
7.7 Exercises 127
8 Additional Results on Options 131
8.1 Introduction 131
8.2 Call Options on Dividend-Paying Securities 131
8.2.1 The Dividend for Each Share of the Security
Is Paid Continuously in Time at a Rate Equal
to a Fixed Fraction / of the Price of the
Security 132
8.2.2 For Each Share Owned, a Single Payment of
fS(td) Is Made at Time td 133
8.2.3 For Each Share Owned, a Fixed Amount D Is
to Be Paid at Time td 134
8.3 Pricing American Put Options 136
8.4 Adding Jumps to Geometric Brownian Motion 142
8.4.1 When the Jump Distribution Is Lognormal 144
8.4.2 When the Jump Distribution Is General 146
8.5 Estimating the Volatility Parameter 148
8.5.1 Estimating a Population Mean and Variance 149
8.5.2 The Standard Estimator of Volatility 150
Contents ix
8.5.3 Using Opening and Closing Data 152
8.5.4 Using Opening, Closing, and High-Low Data 153
8.6 Some Comments 155
8.6.1 When the Option Cost Differs from the
Black-Scholes Formula 155
8.6.2 When the Interest Rate Changes 156
8.6.3 Final Comments 156
8.7 Appendix 158
8.8 Exercises 159
9 Valuing by Expected Utility 165
9.1 Limitations of Arbitrage Pricing 165
9.2 Valuing Investments by Expected Utility 166
9.3 The Portfolio Selection Problem 174
9.3.1 Estimating Covariances 184
9.4 Value at Risk and Conditional Value at Risk 184
9.5 The Capital Assets Pricing Model 187
9.6 Rates of Return: Single-Period and Geometric
Brownian Motion 188
9.7 Exercises 190
10 Stochastic Order Relations 193
10.1 First-Order Stochastic Dominance 193
10.2 Using Coupling to Show Stochastic Dominance 196
10.3 Likelihood Ratio Ordering 198
10.4 A Single-Period Investment Problem 199
10.5 Second-Order Dominance 203
10.5.1 Normal Random Variables 204
10.5.2 More on Second-Order Dominance 207
10.6 Exercises 210
11 Optimization Models 212
11.1 Introduction 212
11.2 A Deterministic Optimization Model 212
11.2.1 A General Solution Technique Based on
Dynamic Programming 213
11.2.2 A Solution Technique for Concave
Return Functions 215
11.2.3 The Knapsack Problem 219
11.3 Probabilistic Optimization Problems 221
x Contents
11.3.1 A Gambling Model with Unknown Win
Probabilities 221
11.3.2 An Investment Allocation Model 222
11.4 Exercises 225
12 Stochastic Dynamic Programming 228
12.1 The Stochastic Dynamic Programming Problem 228
12.2 Infinite Time Models 234
12.3 Optimal Stopping Problems 239
12.4 Exercises 244
13 Exotic Options 247
13.1 Introduction 247
13.2 Barrier Options 247
13.3 Asian and Lookback Options 248
13.4 Monte Carlo Simulation 249
13.5 Pricing Exotic Options by Simulation 250
13.6 More Efficient Simulation Estimators 252
13.6.1 Control and Antithetic Variables in the
Simulation of Asian and Lookback
Option Valuations 253
13.6.2 Combining Conditional Expectation and
Importance Sampling in the Simulation of
Barrier Option Valuations 257
13.7 Options with Nonlinear Payoffs 258
13.8 Pricing Approximations via Multiperiod Binomial
Models 259
13.9 Continuous Time Approximations of Barrier
and Lookback Options 261
13.10 Exercises 262
14 Beyond Geometric Brownian Motion Models 265
14.1 Introduction 265
14.2 Crude Oil Data 266
14.3 Models for the Crude Oil Data 272
14.4 Final Comments 274
15 Autoregressive Models and Mean Reversion 285
15.1 The Autoregressive Model 285
15.2 Valuing Options by Their Expected Return 286
15.3 Mean Reversion 289
15.4 Exercises 291
Index 303
|
| any_adam_object | 1 |
| author | Ross, Sheldon M. 1943- |
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| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| spellingShingle | Ross, Sheldon M. 1943- An elementary introduction to mathematical finance Mathematik Mathematisches Modell Investments Mathematics Stochastic analysis Options (Finance) Mathematical models Securities Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd Optionspreis (DE-588)4115453-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
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| title | An elementary introduction to mathematical finance |
| title_auth | An elementary introduction to mathematical finance |
| title_exact_search | An elementary introduction to mathematical finance |
| title_full | An elementary introduction to mathematical finance Sheldon M. Ross |
| title_fullStr | An elementary introduction to mathematical finance Sheldon M. Ross |
| title_full_unstemmed | An elementary introduction to mathematical finance Sheldon M. Ross |
| title_short | An elementary introduction to mathematical finance |
| title_sort | an elementary introduction to mathematical finance |
| topic | Mathematik Mathematisches Modell Investments Mathematics Stochastic analysis Options (Finance) Mathematical models Securities Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd Optionspreis (DE-588)4115453-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Mathematik Mathematisches Modell Investments Mathematics Stochastic analysis Options (Finance) Mathematical models Securities Prices Mathematical models Optionspreistheorie Optionspreis Finanzmathematik |
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Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 QP 890 R826(3) |
|---|---|
| Copy 1 | ausleihbar Long missing Recall This |