A first course in quantitative finance:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York, NY ; Port Melbourne ; Delhi ; Singapore
Cambridge University Press
2018
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 588 Seiten Illustrationen, Diagramme 25 cm |
| ISBN: | 9781108411431 9781108419574 |
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MARC
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| 100 | 1 | |a Mazzoni, Thomas |e Verfasser |0 (DE-588)173712827 |4 aut | |
| 245 | 1 | 0 | |a A first course in quantitative finance |c Thomas Mazzoni (University of Greifswald) |
| 246 | 1 | 3 | |a Quantitative finance |
| 264 | 1 | |a Cambridge ; New York, NY ; Port Melbourne ; Delhi ; Singapore |b Cambridge University Press |c 2018 | |
| 300 | |a x, 588 Seiten |b Illustrationen, Diagramme |c 25 cm | ||
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Record in the Search Index
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| adam_text | Contents
1 Introduction page 1
About This Book 1
) Technical Basics 5
2 A Primer on Probability 7
2.1 Probability and Measure 7
2.2 Filtrations and the Flow of Information 10
2.3 Conditional Probability and Independence 11
2.4 Random Variables and Stochastic Processes 14
2.5 Moments of Random Variables 17
2.6 Characteristic Function and Fourier-Transform 20
2.7 Further Reading 24
2.8 Problems 24
3 Vector Spaces 26
3.1 Real Vector Spaces 26
3.2 Dual Vector Space and Inner Product 30
3.3 Dimensionality, Basis, and Subspaces 34
3.4 Functionals and Operators 37
3.5 Adjoint and Inverse Operators 43
3.6 Eigenvalue Problems 45
3.7 Linear Algebra 47
3.8 Vector Differential Calculus 53
3.9 Multivariate Normal Distribution 55
3.10 Further Reading 57
3.11 Problems 58
4 Utility Theory 60
4.1 Lotteries 60
4.2 Preference Relations and Expected Utility 61
4.3 Risk Aversion 63
4.4 Measures of Risk Aversion 65
4.5 Certainty Equivalent and Risk Premium 66
4.6 Classes of Utility Functions 68
VI
Contents
4.7 Constrained Optimization 70
4.8 Further Reading 74
4.9 Problems 74
Part II J Financial Markets and Portfolio Theory 77
5 Architecture of Financial Markets 79
5.1 The Arrow-Debreu-World 79
5.2 The Portfolio Selection Problem 81
5.3 Preference-Free Results 83
5.4 Pareto-Optimal Allocation and the Representative Agent 89
5.5 Market Completeness and Replicating Portfolios 92
5.6 Martingale Measures and Duality 96
5.7 Further Reading 97
5.8 Problems 98
6 Modern Portfolio Theory 100
6.1 The Gaussian Framework 100
6.2 Mean-Variance Analysis 104
6.3 The Minimum Variance Portfolio 109
6.4 Variance Efficient Portfolios 111
6.5 Optimal Portfolios and Diversification 113
6.6 Tobin’s Separation Theorem and the Market Portfolio 115
6.7 Further Reading 118
6.8 Problems 119
7 CAPMandAPT 120
7.1 Empirical Problems with MPT 120
7.2 The Capital Asset Pricing Model (CAPM) 121
7.3 Estimating Betas from Market Data 125
7.4 Statistical Issues of Regression Analysis and Inference 129
7.5 The Arbitrage Pricing Theory (APT) 135
7.6 Comparing CAPM and APT 140
7.7 Further Reading 141
7.8 Problems 141
8 Portfolio Performance and Management 143
8.1 Portfolio Performance Statistics 143
8.2 Money Management and Xe/Zy-Criterion 145
8.3 Adjusting for Individual Market Views 150
VII
Contents
8.4 Further Reading 154
8.5 Problems 154
Financial Econcomics 156
9.1 The Rational Valuation Principle 156
9.2 Stock Price Bubbles 160
9.3 Shiller’s Volatility Puzzle 164
9.4 Stochastic Discount Factor Models 166
9.5 C-CAPM and Hansen-Jagannathan-Bounds 169
9.6 The Equity Premium Puzzle 172
9.7 The Campbell-Cochrane-Model 175
9.8 Further Reading 179
9.9 Problems 180
Behavioral Finance 181
10.1 The Efficient Market Hypothesis 181
10.2 Beyond Rationality 185
10.3 Prospect Theory 188
10.4 Cumulative Prospect Theory (CPT) 191
10.5 CPT and the Equity Premium Puzzle 194
10.6 The Price Momentum Effect 197
10.7 Unifying CPT and Modern Portfolio Theory 199
10.8 Further Reading 205
10.9 Problems 205
Part Ni) Derivatives 207
11 Forwards, Futures, and Options 209
11.1 Forward and Future Contracts 209
11.2 Bank Account and Forward Price 210
11.3 Options 213
11.4 Compound Positions and Option Strategies 216
11.5 Arbitrage Bounds on Options 219
11.6 Further Reading 220
11.7 Problems 220
12 The Binomial Model 222
12.1 The Coin Flip Universe 222
12.2 The Multi-Period Binomial Model 225
12.3 Yaluating a European Call in the Binomial Model 228
12.4 Backward Valuation and American Options 232
Contents
12.5 Stopping Times and Sn e//~Envelope 23 5
12.6 Path Dependent Options 240
12.7 The Black-Scholes-Limit of the Binomial Model 243
12.8 Further Reading 246
12.9 Problems 247
13 The Black-Scholes-lheory 249
13.1 Geometric Brownian Motion and Ito’s Lemma 249
13.2 The Black-Scholes-Equalion 253
13.3 Dirac’s ¿-Function and Tempered Distributions 256
13.4 The Fundamental Solution 260
13.5 Binary and Plain Vanilla Option Prices 264
13.6 Simple Extensions of the Black-Scholes-Model 267
13.7 Discrete Dividend Payments 270
13.8 American Exercise Right 274
13.9 Discrete Hedging and the Greeks 277
13.10 Transaction Costs 283
13.11 Merton’s Firm Value Model 287
13.12 Further Reading 289
13.13 Problems 290
14 Exotics in the Black-Scholes-Mode 291
14.1 Finite Difference Methods 291
14.2 Numerical Valuation and Coding 298
14.3 Weak Path Dependence and Early Exercise 301
14.4 Girsanov’s Theorem 303
14.5 The Feynman-Kac-Formula 306
14.6 Monte Carlo Simulation 310
14.7 Strongly Path Dependent Contracts 312
14.8 Valuating American Contracts with Monte Carlo 317
14.9 Further Reading 323
14.10 Problems 323
15 Deterministic Volatility 326
15.1 The Term Structure of Volatility 326
15.2 GARCH-Models 328
15.3 Duan’s Option Pricing Model 332
15.4 Local Volatility and the Dupire-Eqnaiion 334
15.5 Implied Volatility and Most Likely Path 338
15.6 Skew-Based Parametric Representation of the Volatility Surface 343
15.7 Brownian Bridge and GARCH-Parametrization 345
15.8 Further Reading 351
15.9 Problems 351
ix Contents
16 Stochastic Volatility 353
16.1 The Consequence of Stochastic Volatility 353
16.2 Characteristic Functions and the Generalized Fowr/er-Transform 355
16.3 The Pricing Formula in Fourier-Space 358
16.4 The Heston-Nandi GARCH-Model 362
16.5 The Heston-Model 365
16.6 Inverting the Fourier-Transform 370
16.7 Implied Volatility in the SABR-Model 373
16.8 Further Reading 377
16.9 Problems 378
17 Processes with Jumps 379
17.1 Cadlag Processes, Local-, and Semimartingales 379
17.2 Simple and Compound Poisson-Process 381
17.3 GARCH-Models with Conditional Jump Dynamics 385
17.4 Merton’s Jump-Diffusion Model 389
17.5 Barrier Options and the Reflection Principle 393
17.6 Levj-Processes 397
17.7 Subordination of Brownian motion 402
17.8 The Esscher-Transform 406
17.9 Combining Jumps and Stochastic Volatility 410
17.10 Further Reading 412
17.11 Problems 412
Part IV ) The Fixed-Income World 415
18 Basic Fixed-Income Instruments 417
18.1 Bonds and Forward Rate Agreements 417
18.2 LIBOR and Floating Rate Notes 421
18.3 Day-Count Conventions and Accrued Interest 422
18.4 Yield Measures and Yield Curve Construction 425
18.5 Duration and Convexity 430
18.6 Forward Curve and Bootstrapping 433
18.7 Interest Rate Swaps 436
18.8 Further Reading 440
18.9 Problems 440
19 Plain Vanilla Fixed-Income Derivatives 442
19.1 The F-Forward Measure 442
19.2 The Black-7 6-Modd 445
19.3 Caps and Floors 447
Contents
19.4 Swaptions and the Annuity Measure 449
19.5 Eurodollar Futures 452
19.6 Further Reading 453
19.7 Problems 454
20 Term Structure Models 455
20.1 A Term Structure Toy Model 455
20.2 Yield Curve Fitting 458
20.3 Mean Reversion and the Vasicek-Wlo eX 460
20.4 Bond Option Pricing and the /ams/udian-Decomposition 463
20.5 Affine Term Structure Models 465
20.6 The Heath-Jarrow-Morton-Framework 469
20.7 Multi-Factor HJM and Historical Volatility 475
20.8 Further Reading 481
20.9 Problems 481
21 The LIBOR Market Mode! 483
21.1 The Transition from HJM to Market Models 483
21.2 The Change-of-Numeraire Toolkit 487
21.3 Calibration to Caplet Volatilities 491
21.4 Parametric Correlation Matrices 494
21.5 Calibrating Correlations and the Swap Market Model 498
21.6 Pricing Exotics in the LMM 502
21.7 Further Reading 506
21.8 Problems 506
A Complex Analysis 509
A. 1 Introduction to Complex Numbers 509
A.2 Complex Functions and Derivatives 513
A.3 Complex Integration 515
A.4 The Residue Theorem 519
B Solutions to Problems 525
References 573
Index 583
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| isbn | 9781108411431 9781108419574 |
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| spelling | Mazzoni, Thomas Verfasser (DE-588)173712827 aut A first course in quantitative finance Thomas Mazzoni (University of Greifswald) Quantitative finance Cambridge ; New York, NY ; Port Melbourne ; Delhi ; Singapore Cambridge University Press 2018 x, 588 Seiten Illustrationen, Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finance / Mathematical models (DE-588)4123623-3 Lehrbuch gnd-content Finanzmathematik (DE-588)4017195-4 s DE-604 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=030331804&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazzoni, Thomas A first course in quantitative finance Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4123623-3 |
| title | A first course in quantitative finance |
| title_alt | Quantitative finance |
| title_auth | A first course in quantitative finance |
| title_exact_search | A first course in quantitative finance |
| title_full | A first course in quantitative finance Thomas Mazzoni (University of Greifswald) |
| title_fullStr | A first course in quantitative finance Thomas Mazzoni (University of Greifswald) |
| title_full_unstemmed | A first course in quantitative finance Thomas Mazzoni (University of Greifswald) |
| title_short | A first course in quantitative finance |
| title_sort | a first course in quantitative finance |
| topic | Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik Lehrbuch |
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