Financial markets in continuous time:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Berlin ; Heidelberg
Springer
2007
|
| Edition: | corrected second printing |
| Series: | Springer finance textbook
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 326 Seiten |
| ISBN: | 9783540711490 354071149X |
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MARC
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| 240 | 1 | 0 | |a Marchés financiers en temps continu |
| 245 | 1 | 0 | |a Financial markets in continuous time |c Rose-Anne Dana ; Monique Jeanblanc |
| 250 | |a corrected second printing | ||
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2007 | |
| 300 | |a XI, 326 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Springer finance textbook | |
| 650 | 4 | |a Options (Finances) - Modèles mathématiques | |
| 650 | 4 | |a Équilibre (Économie politique) - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Equilibrium (Economics) |x Mathematical models | |
| 650 | 4 | |a Options (Finance) |x Mathematical models | |
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Record in the Search Index
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| adam_text |
Contents
1 The Discrete Case 1
1.1 A Model with Two Dates and Two States of the World 1
1.1.1 The Model 1
1.1.2 Hedging Portfolio, Value of the Option 2
1.1.3 The Risk Neutral Measure, Put Call Parity 4
1.1.4 No Arbitrage Opportunities 5
1.1.5 The Risk Attached to an Option 6
1.1.6 Incomplete Markets 8
1.2 A One Period Model with (d + 1) Assets and k States of the
World 12
1.2.1 No Arbitrage Opportunities 13
1.2.2 Complete Markets 18
1.2.3 Valuation by Arbitrage in the Case of a Complete
Market 19
1.2.4 Incomplete Markets: the Arbitrage Interval 20
1.3 Optimal Consumption and Portfolio Choice in a One Agent
Model 22
1.3.1 The Maximization Problem 23
1.3.2 An Equilibrium Model with a Representative Agent . 28
1.3.3 The Von Neumann Morgenstern Model, Risk Aversion . 30
1.3.4 Optimal Choice in the VNM Model 32
1.3.5 Equilibrium Models with Complete Financial Markets. 36
2 Dynamic Models in Discrete Time 43
2.1 A Model with a Finite Horizon 44
2.2 Arbitrage with a Finite Horizon 45
2.2.1 Arbitrage Opportunities 45
2.2.2 Arbitrage and Martingales 46
2.3 Trees 49
2.4 Complete Markets with a Finite Horizon 53
2.4.1 Characterization 54
VIII Contents
2.5 Valuation 55
2.5.1 The Complete Market Case 56
2.6 An Example 57
2.6.1 The Binomial Model 57
2.6.2 Option Valuation 59
2.6.3 Approaching the Black Scholes Model 60
2.7 Maximization of the Final Wealth 64
2.8 Optimal Choice of Consumption and Portfolio 68
2.9 Infinite Horizon 73
3 The Black Scholes Formula 81
3.1 Stochastic Calculus 81
3.1.1 Brownian Motion and the Stochastic Integral 82
3.1.2 Ito Processes. Girsanov's Theorem 84
3.1.3 Ito's Lemma 85
3.1.4 Multidimensional Processes 87
3.1.5 Multidimensional Ito's Lemma 88
3.1.6 Examples 89
3.2 Arbitrage and Valuation 90
3.2.1 Financing Strategies 90
3.2.2 Arbitrage and the Martingale Measure 92
3.2.3 Valuation 94
3.3 The Black Scholes Formula: the One Dimensional Case 95
3.3.1 The Model 95
3.3.2 The Black Scholes Formula 96
3.3.3 The Risk Neutral Measure 99
3.3.4 Explicit Calculations 101
3.3.5 Comments on the Black Scholes Formula 103
3.4 Extension of the Black Scholes Formula 107
3.4.1 Financing Strategies 107
3.4.2 The State Variable 108
3.4.3 The Black Scholes Formula 109
3.4.4 Special Case Ill
3.4.5 The Risk Neutral Measure Ill
3.4.6 Example 113
3.4.7 Applications of the Black Scholes Formula 113
4 Portfolios Optimizing Wealth and Consumption 127
4.1 The Model 127
4.2 Optimization 130
4.3 Solution in the Case of Constant Coefficients 130
4.3.1 Dynamic Programming 130
4.3.2 The Hamilton Jacobi Bellman Equation 131
4.3.3 A Special Case 136
4.4 Admissible Strategies 137
Contents IX
4.5 Existence of an Optimal Pair 141
4.5.1 Construction of an Optimal Pair 142
4.5.2 The Value Function 144
4.5.3 A Special Case 145
4.6 Solution in the Case of Deterministic Coefficients 147
4.6.1 The Value Function and Partial Differential Equations . 148
4.6.2 Optimal Wealth 149
4.6.3 Obtaining the Optimal Portfolio 150
4.7 Market Completeness and NAO 151
5 The Yield Curve 159
5.1 Discrete Time Model 159
5.2 Continuous Time Model 164
5.2.1 Definitions 164
5.2.2 Change of Numeraire 166
5.2.3 Valuation of an Option on a Coupon Bond 171
5.3 The Heath Jarrow Morton Model 172
5.3.1 The Model 172
5.3.2 The Linear Gaussian Case 174
5.4 When the Spot Rate is Given 179
5.5 The Vasicek Model 181
5.5.1 The Ornstein Uhlenbeck Process 181
5.5.2 Determining P(t, T) when q is Constant 183
5.6 The Cox Ingersoll Ross Model 185
5.6.1 The Cox Ingersoll Ross Process 185
5.6.2 Valuation of a Zero Coupon Bond 187
6 Equilibrium of Financial Markets in Discrete Time 191
6.1 Equilibrium in a Static Exchange Economy 192
6.2 The Demand Approach 194
6.3 The Negishi Method 196
6.3.1 Pareto Optima 196
6.3.2 Two Characterizations of Pareto Optima 197
6.3.3 Existence of an Equilibrium 200
6.4 The Theory of Contingent Markets 201
6.5 The Arrow Radner Equilibrium Exchange Economy with
Financial Markets with Two Dates 203
6.6 The Complete Markets Case 205
6.7 The CAPM 208
7 Equilibrium of Financial Markets in Continuous Time.
The Complete Markets Case 217
7.1 The Model 217
7.1.1 The Financial Market 218
7.1.2 The Economy 219
X Contents
7.1.3 Admissible Pairs 220
7.1.4 Definition and Existence of a Radner Equilibrium 222
7.2 Existence of a Contingent Arrow Debreu Equilibrium 224
7.2.1 Aggregate Utility 224
7.2.2 Definition and Characterization of Pareto Optima 225
7.2.3 Existence and Characterization of a Contingent
Arrow Debreu Equilibrium 228
7.2.4 Existence of a Radner Equilibrium 228
7.3 Applications 230
7.3.1 Arbitrage Price of Real Secondary Assets. Lucas'
Formula 230
7.3.2 CCAPM (Consumption based Capital Asset Pricing
Model) 232
8 Incomplete Markets 237
8.1 Incomplete Markets 237
8.1.1 The Case of Constant Coefficients 237
8.1.2 No Arbitrage Markets 239
8.1.3 The Price Range 240
8.1.4 Superhedging 242
8.1.5 The Minimal Probability Measure 243
8.1.6 Valuation Using Utility Functions 244
8.1.7 Transaction Costs 245
8.2 Stochastic Volatility 245
8.2.1 The Robustness of the Black Scholes Formula 246
8.3 Wealth Optimization 247
9 Exotic Options 249
9.1 The Hitting Time and Supremum for Brownian Motion 250
9.1.1 Distribution of the Pair (Bt, Mt) 250
9.1.2 Distribution of Sup and of the Hitting Time 251
9.1.3 Distribution of Inf 252
9.1.4 Laplace Tranforms 252
9.1.5 Hitting Time for a Double Barrier 253
9.2 Drifted Brownian Motion 254
9.2.1 The Laplace Transform of a Hitting Time 254
9.2.2 Distribution of the Pair (Maximum, Minimum) 255
9.2.3 Evaluation of E(e rTy ITy o) 255
9.3 Barrier Options 256
9.3.1 Down and Out Options 256
9.3.2 Down and In Options 257
9.3.3 Up and Out and Up and In Options 257
9.3.4 Intermediate Calculations 257
9.3.5 The Value of the Compensation 260
9.3.6 Valuation of a DIC Option 261
Contents XI
9.3.7 Up and In Options 263
9.3.8 P. Carr 's Symmetry 264
9.4 Double Barriers 267
9.5 Lookback Options 269
9.6 Other Options 271
9.6.1 Options Linked to the Hitting Time of a Barrier 271
9.6.2 Options Linked to Occupation Times 272
9.7 Other Products 274
9.7.1 Asian Options or Average Rate Options 274
9.7.2 Products Depending on an Interim Date 275
9.7.3 Still More Products 275
A Brownian Motion 279
A.I Historical Background 279
A.2 Intuition 279
A.3 Random Walk 280
A.4 The Stochastic Integral 283
A.5 Ito's Formula 285
B Numerical Methods 287
B.I Finite Difference 288
B.I.I Method 289
B.1.2 The Implicit Scheme Case 290
B.I.3 Solving the System 291
B.1.4 Other Schemes 292
B.2 Extrapolation Methods 292
B.2.1 The Heat Equation 293
B.2.2 Approximations 293
B.3 Simulation 294
B.3.1 Simulation of the Uniform Distribution on [0,1] 295
B.3.2 Simulation of Discrete Variables 295
B.3.3 Simulation of a Random Variable 295
B.3.4 Simulation of an Expectation 296
B.3.5 Simulation of a Brownian Motion 297
B.3.6 Simulation of Solutions to Stochastic Differential
Equations 298
B.3.7 Calculating E(f(Xt)) 299
References 301
Index 323 |
| adam_txt |
Contents
1 The Discrete Case 1
1.1 A Model with Two Dates and Two States of the World 1
1.1.1 The Model 1
1.1.2 Hedging Portfolio, Value of the Option 2
1.1.3 The Risk Neutral Measure, Put Call Parity 4
1.1.4 No Arbitrage Opportunities 5
1.1.5 The Risk Attached to an Option 6
1.1.6 Incomplete Markets 8
1.2 A One Period Model with (d + 1) Assets and k States of the
World 12
1.2.1 No Arbitrage Opportunities 13
1.2.2 Complete Markets 18
1.2.3 Valuation by Arbitrage in the Case of a Complete
Market 19
1.2.4 Incomplete Markets: the Arbitrage Interval 20
1.3 Optimal Consumption and Portfolio Choice in a One Agent
Model 22
1.3.1 The Maximization Problem 23
1.3.2 An Equilibrium Model with a Representative Agent . 28
1.3.3 The Von Neumann Morgenstern Model, Risk Aversion . 30
1.3.4 Optimal Choice in the VNM Model 32
1.3.5 Equilibrium Models with Complete Financial Markets. 36
2 Dynamic Models in Discrete Time 43
2.1 A Model with a Finite Horizon 44
2.2 Arbitrage with a Finite Horizon 45
2.2.1 Arbitrage Opportunities 45
2.2.2 Arbitrage and Martingales 46
2.3 Trees 49
2.4 Complete Markets with a Finite Horizon 53
2.4.1 Characterization 54
VIII Contents
2.5 Valuation 55
2.5.1 The Complete Market Case 56
2.6 An Example 57
2.6.1 The Binomial Model 57
2.6.2 Option Valuation 59
2.6.3 Approaching the Black Scholes Model 60
2.7 Maximization of the Final Wealth 64
2.8 Optimal Choice of Consumption and Portfolio 68
2.9 Infinite Horizon 73
3 The Black Scholes Formula 81
3.1 Stochastic Calculus 81
3.1.1 Brownian Motion and the Stochastic Integral 82
3.1.2 Ito Processes. Girsanov's Theorem 84
3.1.3 Ito's Lemma 85
3.1.4 Multidimensional Processes 87
3.1.5 Multidimensional Ito's Lemma 88
3.1.6 Examples 89
3.2 Arbitrage and Valuation 90
3.2.1 Financing Strategies 90
3.2.2 Arbitrage and the Martingale Measure 92
3.2.3 Valuation 94
3.3 The Black Scholes Formula: the One Dimensional Case 95
3.3.1 The Model 95
3.3.2 The Black Scholes Formula 96
3.3.3 The Risk Neutral Measure 99
3.3.4 Explicit Calculations 101
3.3.5 Comments on the Black Scholes Formula 103
3.4 Extension of the Black Scholes Formula 107
3.4.1 Financing Strategies 107
3.4.2 The State Variable 108
3.4.3 The Black Scholes Formula 109
3.4.4 Special Case Ill
3.4.5 The Risk Neutral Measure Ill
3.4.6 Example 113
3.4.7 Applications of the Black Scholes Formula 113
4 Portfolios Optimizing Wealth and Consumption 127
4.1 The Model 127
4.2 Optimization 130
4.3 Solution in the Case of Constant Coefficients 130
4.3.1 Dynamic Programming 130
4.3.2 The Hamilton Jacobi Bellman Equation 131
4.3.3 A Special Case 136
4.4 Admissible Strategies 137
Contents IX
4.5 Existence of an Optimal Pair 141
4.5.1 Construction of an Optimal Pair 142
4.5.2 The Value Function 144
4.5.3 A Special Case 145
4.6 Solution in the Case of Deterministic Coefficients 147
4.6.1 The Value Function and Partial Differential Equations . 148
4.6.2 Optimal Wealth 149
4.6.3 Obtaining the Optimal Portfolio 150
4.7 Market Completeness and NAO 151
5 The Yield Curve 159
5.1 Discrete Time Model 159
5.2 Continuous Time Model 164
5.2.1 Definitions 164
5.2.2 Change of Numeraire 166
5.2.3 Valuation of an Option on a Coupon Bond 171
5.3 The Heath Jarrow Morton Model 172
5.3.1 The Model 172
5.3.2 The Linear Gaussian Case 174
5.4 When the Spot Rate is Given 179
5.5 The Vasicek Model 181
5.5.1 The Ornstein Uhlenbeck Process 181
5.5.2 Determining P(t, T) when q is Constant 183
5.6 The Cox Ingersoll Ross Model 185
5.6.1 The Cox Ingersoll Ross Process 185
5.6.2 Valuation of a Zero Coupon Bond 187
6 Equilibrium of Financial Markets in Discrete Time 191
6.1 Equilibrium in a Static Exchange Economy 192
6.2 The Demand Approach 194
6.3 The Negishi Method 196
6.3.1 Pareto Optima 196
6.3.2 Two Characterizations of Pareto Optima 197
6.3.3 Existence of an Equilibrium 200
6.4 The Theory of Contingent Markets 201
6.5 The Arrow Radner Equilibrium Exchange Economy with
Financial Markets with Two Dates 203
6.6 The Complete Markets Case 205
6.7 The CAPM 208
7 Equilibrium of Financial Markets in Continuous Time.
The Complete Markets Case 217
7.1 The Model 217
7.1.1 The Financial Market 218
7.1.2 The Economy 219
X Contents
7.1.3 Admissible Pairs 220
7.1.4 Definition and Existence of a Radner Equilibrium 222
7.2 Existence of a Contingent Arrow Debreu Equilibrium 224
7.2.1 Aggregate Utility 224
7.2.2 Definition and Characterization of Pareto Optima 225
7.2.3 Existence and Characterization of a Contingent
Arrow Debreu Equilibrium 228
7.2.4 Existence of a Radner Equilibrium 228
7.3 Applications 230
7.3.1 Arbitrage Price of Real Secondary Assets. Lucas'
Formula 230
7.3.2 CCAPM (Consumption based Capital Asset Pricing
Model) 232
8 Incomplete Markets 237
8.1 Incomplete Markets 237
8.1.1 The Case of Constant Coefficients 237
8.1.2 No Arbitrage Markets 239
8.1.3 The Price Range 240
8.1.4 Superhedging 242
8.1.5 The Minimal Probability Measure 243
8.1.6 Valuation Using Utility Functions 244
8.1.7 Transaction Costs 245
8.2 Stochastic Volatility 245
8.2.1 The Robustness of the Black Scholes Formula 246
8.3 Wealth Optimization 247
9 Exotic Options 249
9.1 The Hitting Time and Supremum for Brownian Motion 250
9.1.1 Distribution of the Pair (Bt, Mt) 250
9.1.2 Distribution of Sup and of the Hitting Time 251
9.1.3 Distribution of Inf 252
9.1.4 Laplace Tranforms 252
9.1.5 Hitting Time for a Double Barrier 253
9.2 Drifted Brownian Motion 254
9.2.1 The Laplace Transform of a Hitting Time 254
9.2.2 Distribution of the Pair (Maximum, Minimum) 255
9.2.3 Evaluation of E(e rTy ITy o) 255
9.3 Barrier Options 256
9.3.1 Down and Out Options 256
9.3.2 Down and In Options 257
9.3.3 Up and Out and Up and In Options 257
9.3.4 Intermediate Calculations 257
9.3.5 The Value of the Compensation 260
9.3.6 Valuation of a DIC Option 261
Contents XI
9.3.7 Up and In Options 263
9.3.8 P. Carr 's Symmetry 264
9.4 Double Barriers 267
9.5 Lookback Options 269
9.6 Other Options 271
9.6.1 Options Linked to the Hitting Time of a Barrier 271
9.6.2 Options Linked to Occupation Times 272
9.7 Other Products 274
9.7.1 Asian Options or Average Rate Options 274
9.7.2 Products Depending on an Interim Date 275
9.7.3 Still More Products 275
A Brownian Motion 279
A.I Historical Background 279
A.2 Intuition 279
A.3 Random Walk 280
A.4 The Stochastic Integral 283
A.5 Ito's Formula 285
B Numerical Methods 287
B.I Finite Difference 288
B.I.I Method 289
B.1.2 The Implicit Scheme Case 290
B.I.3 Solving the System 291
B.1.4 Other Schemes 292
B.2 Extrapolation Methods 292
B.2.1 The Heat Equation 293
B.2.2 Approximations 293
B.3 Simulation 294
B.3.1 Simulation of the Uniform Distribution on [0,1] 295
B.3.2 Simulation of Discrete Variables 295
B.3.3 Simulation of a Random Variable 295
B.3.4 Simulation of an Expectation 296
B.3.5 Simulation of a Brownian Motion 297
B.3.6 Simulation of Solutions to Stochastic Differential
Equations 298
B.3.7 Calculating E(f(Xt)) 299
References 301
Index 323 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Dana, Rose-Anne Jeanblanc, Monique 1947- |
| author_GND | (DE-588)170731227 (DE-588)171430689 |
| author_facet | Dana, Rose-Anne Jeanblanc, Monique 1947- |
| author_role | aut aut |
| author_sort | Dana, Rose-Anne |
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| building | Verbundindex |
| bvnumber | BV022542198 |
| callnumber-first | H - Social Science |
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| callnumber-search | HG6024.A3 |
| callnumber-sort | HG 46024 A3 |
| callnumber-subject | HG - Finance |
| classification_rvk | QK 660 SK 820 SK 980 |
| ctrlnum | (OCoLC)184698482 (DE-599)DNB983898588 |
| dewey-full | 332.64530151923 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.64530151923 |
| dewey-search | 332.64530151923 |
| dewey-sort | 3332.64530151923 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | corrected second printing |
| format | Book |
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| id | DE-604.BV022542198 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:10:39Z |
| indexdate | 2024-07-20T09:21:06Z |
| institution | BVB |
| isbn | 9783540711490 354071149X |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015748614 |
| oclc_num | 184698482 |
| open_access_boolean | |
| owner | DE-N2 DE-703 DE-11 DE-20 DE-521 DE-83 |
| owner_facet | DE-N2 DE-703 DE-11 DE-20 DE-521 DE-83 |
| physical | XI, 326 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer finance textbook |
| spelling | Dana, Rose-Anne (DE-588)170731227 aut Marchés financiers en temps continu Financial markets in continuous time Rose-Anne Dana ; Monique Jeanblanc corrected second printing Berlin ; Heidelberg Springer 2007 XI, 326 Seiten txt rdacontent n rdamedia nc rdacarrier Springer finance textbook Options (Finances) - Modèles mathématiques Équilibre (Économie politique) - Modèles mathématiques Mathematisches Modell Equilibrium (Economics) Mathematical models Options (Finance) Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 s Arbitrage-Pricing-Theorie (DE-588)4112584-8 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Jeanblanc, Monique 1947- (DE-588)171430689 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2944341&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015748614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dana, Rose-Anne Jeanblanc, Monique 1947- Financial markets in continuous time Options (Finances) - Modèles mathématiques Équilibre (Économie politique) - Modèles mathématiques Mathematisches Modell Equilibrium (Economics) Mathematical models Options (Finance) Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd Stochastisches Modell (DE-588)4057633-4 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd |
| subject_GND | (DE-588)4135346-8 (DE-588)4057633-4 (DE-588)4112584-8 |
| title | Financial markets in continuous time |
| title_alt | Marchés financiers en temps continu |
| title_auth | Financial markets in continuous time |
| title_exact_search | Financial markets in continuous time |
| title_exact_search_txtP | Financial markets in continuous time |
| title_full | Financial markets in continuous time Rose-Anne Dana ; Monique Jeanblanc |
| title_fullStr | Financial markets in continuous time Rose-Anne Dana ; Monique Jeanblanc |
| title_full_unstemmed | Financial markets in continuous time Rose-Anne Dana ; Monique Jeanblanc |
| title_short | Financial markets in continuous time |
| title_sort | financial markets in continuous time |
| topic | Options (Finances) - Modèles mathématiques Équilibre (Économie politique) - Modèles mathématiques Mathematisches Modell Equilibrium (Economics) Mathematical models Options (Finance) Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd Stochastisches Modell (DE-588)4057633-4 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd |
| topic_facet | Options (Finances) - Modèles mathématiques Équilibre (Économie politique) - Modèles mathématiques Mathematisches Modell Equilibrium (Economics) Mathematical models Options (Finance) Mathematical models Optionspreistheorie Stochastisches Modell Arbitrage-Pricing-Theorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2944341&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015748614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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