Stochastic analysis for finance with simulations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Cham]
Springer
[2016]
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis |
| Beschreibung: | xxxii, 657 Seiten Diagramme (teilweise farbig) |
| ISBN: | 9783319255873 |
| ISSN: | 0172-5939 |
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| 100 | 1 | |a Choe, Geon Ho |e Verfasser |0 (DE-588)1011618036 |4 aut | |
| 245 | 1 | 0 | |a Stochastic analysis for finance with simulations |c Geon Ho Choe |
| 264 | 1 | |a [Cham] |b Springer |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xxxii, 657 Seiten |b Diagramme (teilweise farbig) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 0 | 7 | |a Simulation |0 (DE-588)4055072-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 653 | |a Lower undergraduate | ||
| 653 | |a PB | ||
| 653 | |a Martingale Method | ||
| 653 | |a Binomial Tree Method | ||
| 653 | |a Optimal Portfolio | ||
| 653 | |a Time Series | ||
| 653 | |a Brownian Motion | ||
| 653 | |a Stochastic Differential Equation | ||
| 653 | |a Option Pricing | ||
| 653 | |a Monte Carlo Method | ||
| 653 | |a Black–Scholes–Merton Equation | ||
| 653 | |a Interest Rate Model | ||
| 653 | |a Stochastic Calculus | ||
| 689 | 0 | 0 | |a Kapitalmarkttheorie |0 (DE-588)4137411-3 |D s |
| 689 | 0 | 1 | |a Finanzmathematik |0 (DE-588)4017195-4 |D s |
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| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1806333992159412224 |
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Contents
Part I Introduction to Financial Mathematics
1 Fundamental Concepts .
1.1 Risk.
1.2 Time Value of Money.
1.3 No Arbitrage Principle.
1.4 Arbitrage Free Market.
1.5 Risk-Neutral Pricing and Martingale Measures
1.6 The One Period Binomial Tree Model.
1.7 Models in Finance.
2 Financial Derivatives.
2.1 Forward Contracts and Futures.
2.2 Options.
2.3 Put-Call Parity .
2.4 Relations Among Option Pricing Methods.
Part II Probability Theory
3 The Lebesgue Integral.
3.1 Measures.
3.2 Simple Functions.
3.3 The Lebesgue Integral.
3.4 Inequalities.
3.5 The Radon-Nikodym Theorem.
3.6 Computer Experiments.
4 Basic Probability Theory.
4.1 Measure and Probability.
4.2 Characteristic Functions.
4.3 Independent Random Variables.
4.4 Change of Variables.
4.5 The Law of Large Numbers.
4.6 The Central Limit Theorem.
x Contents
4.7 Statistical Ideas. 63
4.8 Computer Experiments. 67
5 Conditional Expectation. 75
5.1 Conditional Expectation Given an Event. 75
5.2 Conditional Expectation with Respect to a o-Algebra. 76
5.3 Conditional Expectation with Respect to a Random Variable. 84
5.4 Computer Experiments. 86
6 Stochastic Processes. 91
6.1 Stochastic Processes. 91
6.2 Predictable Processes. 93
6.3 Martingales. 95
6.4 Stopping Time. 102
6.5 Computer Experiments. 105
Part III Brownian Motion
7 Brownian Motion. Ill
7.1 Brownian Motion as a Stochastic Process. Ill
7.2 Sample Paths of Brownian Motion. 121
7.3 Brownian Motion and Martingales. 127
7.4 Computer Experiments. 132
8 Girsanov’s Theorem. 137
8.1 Motivation. 137
8.2 Equivalent Probability Measure. 140
8.3 Brownian Motion with Drift. 141
8.4 Computer Experiments. 143
9 The Reflection Principle of Brownian Motion. 147
9.1 The Reflection Property of Brownian Motion. 147
9.2 The Maximum of Brownian Motion. 149
9.3 The Maximum of Brownian Motion with Drift. 151
9.4 Computer Experiments. 155
Part IV Ito Calculus
10 The Ito Integral. 159
10.1 Definition of the Ito Integral. 159
10.2 The Martingale Property of the Ito Integral. 166
10.3 Stochastic Integrals with Respect to a Martingale. 167
10.4 The Martingale Representation Theorem. 170
10.5 Computer Experiments. 171
11 The Ito Formula. 177
11.1 Motivation for the Ito Formula. 177
11.2 The Ito Formula: Basic Form. 183
Contents
xi
11.3 The Ito Formula: General Form. 189
11.4 Multidimensional Brownian Motion and the Ito Formula. 197
11.5 Computer Experiments. 199
12 Stochastic Differential Equations . 203
12.1 Strong Solutions . 204
12.2 Weak Solutions. 208
12.3 Brownian Bridges. 210
12.4 Computer Experiments. 218
13 The Feynman-Kac Theorem . 225
13.1 The Feynman-Kac Theorem. 225
13.2 Application to the Black-Scholes-Merton Equation. 228
13.3 The Kolmogorov Equations. 229
13.4 Computer Experiments. 234
Part V Option Pricing Methods
14 The Binomial Tree Method for Option Pricing . 239
14.1 Motivation for the Binomial Tree Method. 239
14.2 The One Period Binomial Tree Method . 240
14.2.1 Pricing by Hedging . 240
14.2.2 Pricing by Replication. 242
14.3 The Multiperiod Binomial Tree Method. 243
14.4 Convergence to the Black-Scholes-Merton Formula. 247
14.5 Computer Experiments. 251
15 The Black-Scholes-Merton Differential Equation . 255
15.1 Derivation of the Black-Scholes-Merton Differential Equation. 255
15.2 Price of a European Call Option . 258
15.3 Greeks. 264
15.4 Solution by the Laplace Transform. 269
15.5 Computer Experiments. 273
16 The Martingale Method . 281
16.1 Option Pricing by the Martingale Method. 281
16.2 The Probability Distribution of Asset Price . 286
16.3 The Black-Scholes-Merton Formula. 287
16.4 Derivation of the Black-Scholes-Merton Equation. 288
16.5 Delta Hedging. 290
16.6 Computer Experiments. 292
Contents
xii
Part VI Examples of Option Pricing
17 Pricing of Vanilla Options . 297
17.1 Stocks with a Dividend. 297
17.2 Bonds with Coupons. 301
17.3 Binary Options. 302
17.4 Computer Experiments. 316
18 Pricing of Exotic Options . 321
18.1 Asian Options. 321
18.2 Barrier Options. 325
18.3 Computer Experiments. 334
19 American Options . 337
19.1 American Cali Options. 337
19.2 American Put Options. 338
19.3 The Least Squares Method of Longstaff and Schwartz. 341
19.4 Computer Experiments. 345
Part VII Portfolio Management
20 The Capital Asset Pricing Model. 353
20.1 Return Rate and the Covariance Matrix . 353
20.2 Portfolios of Two Assets and More. 356
20.3 An Application of the Lagrange Multiplier Method. 360
20.4 Minimum Variance Line. 362
20.5 The Efficient Frontier. 367
20.6 The Market Portfolio . 369
20.7 The Beta Coefficient. 373
20.8 Computer Experiments. 374
21 Dynamic Programming . 379
21.1 The Hamilton-Jacobi-Bellman Equation. 379
21.2 Portfolio Management for Optimal Consumption. 382
21.3 Computer Experiments. 391
Part VIII Interest Rate Models
22 Bond Pricing. 397
22.1 Periodic and Continuous Compounding. 397
22.2 Zero Coupon Interest Rates . 398
22.3 Term Structure of Interest Rates . 400
22.4 Forward Rates. 402
22.5 Yield to Maturity. 403
22.6 Duration. 404
22.7 Definitions of Various Interest Rates. 407
22.8 The Fundamental Equation for Bond Pricing. 409
22.9 Computer Experiments. 416
Contents
xin
23 Interest Rate Models. 421
23.1 Short Rate Models. 421
23.2 The Vasicek Model . 422
23.3 The Cox-Ingersoll-Ross Model . 427
23.4 The Ho-Lee Model. 431
23.5 The Hull-White Model. 433
23.6 Computer Experiments. 434
24 Numeraires. 443
24.1 Change of Numeraire for a Binomial Tree Model. 443
24.2 Change of Numeraire for Continuous Time. 445
24.3 Numeraires for Pricing of Interest Rate Derivatives. 451
Part IX Computational Methods
25 Numerical Estimation of Volatility. 457
25.1 Historical Volatility. 457
25.2 Implied Volatility . 459
25.2.1 The Bisection Method . 459
25.2.2 The Newton-Raphson Method. 460
25.3 Computer Experiments. 465
26 Time Series —. 469
26.1 The Cobweb Model. 469
26.2 The Spectral Theory of Time Series. 472
26.3 Autoregressive and Moving Average Models . 476
26.4 Time Series Models for Volatility. 478
26.5 Computer Experiments. 482
27 Random Numbers . 487
27.1 What Is a Monte Carlo Method?. 487
27.2 Uniformly Distributed Random Numbers. 489
27.3 Testing Random Number Generators. 490
27.4 Normally Distributed Random Numbers. 491
27.5 Computer Experiments. 495
28 The Monte Carlo Method for Option Pricing . 501
28.1 The Antithetic Variate Method. 501
28.2 The Control Variate Method. 505
28.3 The Importance Sampling Method. 508
28.4 Computer Experiments. 511
29 Numerical Solution of the Black-Scholes-Merton Equation . 519
29.1 Difference Operators. 519
29.2 Grid and Finite Difference Methods. 521
29.2.3 Explicit Method. 522
29.2.2 Implicit Method. 526
29.2.3 Crank-Nicolson Method. 528
xiv Contents
29.3 Numerical Methods for the Black-Scholes-Merton Equation. 529
29.4 Stability. 529
29.5 Computer Experiments. 531
30 Numerical Solution of Stochastic Differential Equations. 535
30.1 Discretization of Stochastic Differential Equations. 535
30.2 Stochastic Taylor Series. 537
30.2.1 Taylor Series for an Ordinary Differential Equation. 537
30.2.2 Taylor Series for a Stochastic Differential Equation. 538
30.3 The Euler Scheme. 541
30.4 The Milstein Scheme. 542
30.5 Computer Experiments. 543
A Basic Analysis. 545
A. 1 Sets and Functions. 545
A.2 Metric Spaces. 546
A.3 Continuous Functions. 547
A.4 Bounded Linear Transformations. 549
A.5 Extension of a Function . 552
A. 6 Differentiation of a Function. 553
B Linear Algebra . 555
B. l Vectors. 555
B.2 Matrices. 556
B.3 The Method of Least Squares. 557
B.4 Symmetric Matrices . 560
B.5 Principal Component Analysis (PCA). 561
B.6 Tridiagonal Matrices.— 562
B. 7 Convergence of Iterative Algorithms . 564
C Ordinary Differential Equations . 567
C. 1 Linear Differential Equations with Constant Coefficients. 567
C.2 Linear Differential Equations with Nonconstant Coefficients. 569
C.3 Nonlinear Differential Equations. 570
C.4 Ordinary Differential Equations Defined by Vector Fields. 571
C. 5 Infinitesimal Generators for Vector Fields. 572
D Diffusion Equations. 575
D. 1 Examples of Partial Differential Equations. 575
D.2 The Fourier Transform. 576
D.3 The Laplace Transform. 577
D. 4 The Boundary Value Problem for Diffusion Equations. 581
E Entropy . 583
E. 1 What Is Entropy? . 583
E.2 The Maximum Entropy Principle. 584
Contents
xv
F Matlajb Programming. 591
F.l How to Start. 591
F.2 Random Numbers. 593
F.3 Vectors and Matrices. 593
F.4 Tridiagonal Matrices. 596
F.5 Loops for Iterative Algorithms. 597
F.6 How to Plot Graphs .,. 598
F.7 Curve Fitting. 599
F.8 How to Define a Function. 599
F.9 Statistics. 601
Solutions for Selected Problems. 603
Glossary. 637
References. 647
Index
651 |
| any_adam_object | 1 |
| author | Choe, Geon Ho |
| author_GND | (DE-588)1011618036 |
| author_facet | Choe, Geon Ho |
| author_role | aut |
| author_sort | Choe, Geon Ho |
| author_variant | g h c gh ghc |
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| bvnumber | BV043704876 |
| classification_rvk | QP 890 SK 820 SK 980 |
| ctrlnum | (OCoLC)957765002 (DE-599)DNB1076582885 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV043704876 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-03T03:05:34Z |
| institution | BVB |
| institution_GND | (DE-588)1064344704 |
| isbn | 9783319255873 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029117213 |
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| physical | xxxii, 657 Seiten Diagramme (teilweise farbig) |
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| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Choe, Geon Ho Verfasser (DE-588)1011618036 aut Stochastic analysis for finance with simulations Geon Ho Choe [Cham] Springer [2016] © 2016 xxxii, 657 Seiten Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Universitext 0172-5939 Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Kapitalmarkttheorie (DE-588)4137411-3 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Lower undergraduate PB Martingale Method Binomial Tree Method Optimal Portfolio Time Series Brownian Motion Stochastic Differential Equation Option Pricing Monte Carlo Method Black–Scholes–Merton Equation Interest Rate Model Stochastic Calculus Kapitalmarkttheorie (DE-588)4137411-3 s Finanzmathematik (DE-588)4017195-4 s Stochastische Analysis (DE-588)4132272-1 s Simulation (DE-588)4055072-2 s DE-604 Springer International Publishing (DE-588)1064344704 pbl Erscheint auch als eBook 10.1007/978-3-319-25589-7 978-3-319-25589-7 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=62f9df3402c64faaafe86570b26cd277&prov=M&dok_var=1&dok_ext=htm Inhaltstext http://www.springer.com/ Verlag 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=029117213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Choe, Geon Ho Stochastic analysis for finance with simulations Stochastische Analysis (DE-588)4132272-1 gnd Kapitalmarkttheorie (DE-588)4137411-3 gnd Simulation (DE-588)4055072-2 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4137411-3 (DE-588)4055072-2 (DE-588)4017195-4 |
| title | Stochastic analysis for finance with simulations |
| title_auth | Stochastic analysis for finance with simulations |
| title_exact_search | Stochastic analysis for finance with simulations |
| title_full | Stochastic analysis for finance with simulations Geon Ho Choe |
| title_fullStr | Stochastic analysis for finance with simulations Geon Ho Choe |
| title_full_unstemmed | Stochastic analysis for finance with simulations Geon Ho Choe |
| title_short | Stochastic analysis for finance with simulations |
| title_sort | stochastic analysis for finance with simulations |
| topic | Stochastische Analysis (DE-588)4132272-1 gnd Kapitalmarkttheorie (DE-588)4137411-3 gnd Simulation (DE-588)4055072-2 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Stochastische Analysis Kapitalmarkttheorie Simulation Finanzmathematik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=62f9df3402c64faaafe86570b26cd277&prov=M&dok_var=1&dok_ext=htm http://www.springer.com/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029117213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT choegeonho stochasticanalysisforfinancewithsimulations AT springerinternationalpublishing stochasticanalysisforfinancewithsimulations |