Pricing derivatives: the financial concepts underlying the mathematics of pricing derivatives
Irwin Library of Investment and Finance Pricing Derivatives provides investors with a clear understanding of derivative pricing models by first focusing on the underlying mathematics and financial concepts upon which the models were originally built. Trading consultant Professor Ambar Sengupta uses...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
c2005
|
| Schriftenreihe: | The McGraw-Hill library of investment and finance
|
| Schlagworte: | |
| Online-Zugang: | Table of contents Contributor biographical information Publisher description Inhaltsverzeichnis |
| Zusammenfassung: | Irwin Library of Investment and Finance Pricing Derivatives provides investors with a clear understanding of derivative pricing models by first focusing on the underlying mathematics and financial concepts upon which the models were originally built. Trading consultant Professor Ambar Sengupta uses short, to-the-point chapters to examine the relation between price and probability as well as pricing structures of all major derivative instruments. Other topics covered include foundations of stochastic models of pricing, along with methods for establishing optimal prices in terms of the max-min principles that underlie game theory. |
| Beschreibung: | Includes bibliographical references (p. 269-271) and index |
| Beschreibung: | xiv, 282 p. 24 cm |
| ISBN: | 0071445889 |
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| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c c2005 | |
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| 490 | 0 | |a The McGraw-Hill library of investment and finance | |
| 500 | |a Includes bibliographical references (p. 269-271) and index | ||
| 520 | 3 | |a Irwin Library of Investment and Finance Pricing Derivatives provides investors with a clear understanding of derivative pricing models by first focusing on the underlying mathematics and financial concepts upon which the models were originally built. Trading consultant Professor Ambar Sengupta uses short, to-the-point chapters to examine the relation between price and probability as well as pricing structures of all major derivative instruments. Other topics covered include foundations of stochastic models of pricing, along with methods for establishing optimal prices in terms of the max-min principles that underlie game theory. | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS LIST OF TABLES xi
PREFACE xiii
PART ONE FUNDAMENTALS
Chapter 1
Price and Probability 3
An Option Pricing Formula 5
Chapter 2
The Market Equilibrium Measure 9
Chapter 3
Price as Expectation 13
Chapter 4
Changing Numeraires 15
Chapter 5
Changing Numeraires: Examples 19
Fixed Exchange Rate 19
The Log Normal Case 20
Chapter 6 No Arbitrage and the Min Max Argument 23
No Arbitrage and the Pricing Measure 24
Proof of Theorem 6.1.1 26
V
vi Contents
Uniqueness I Nonuniqueness of the Measure Q 29
The Central Idea: The Max Min Argument 30
A Formal Framework 30
Chapter 7
Conditional Price as Conditional Expectation: The
Martingale Principle 39
Conditional Probabilities and Expectations 39
The Generalized Martingale Principle 41
The Discounted Price Process as a Martingale 41
Change of Numeraire Revisited 43
PART TWO
PRICES OF BASIC INSTRUMENTS
Chapter 8
Bonds and Interest 47
Zero Coupon Default Free Bond Prices 48
Assets with Default Risk 50
Credit Default Swaps: CDS 53
Chapter 9
Forward Prices 55
Chapter 10
Futures Prices 61
The Futures Agreement 62
Futures Prices in the Discrete Case 62
Futures Prices in the Continuous Case 63
Chapter 11
Calls and Puts 67
Options: A Closer Look 69
Call Price 72
Contents vii
Put Price 75
Put Call Parity 76
Another Proof of the Option Price Formula 76
Option Price Inequalities 77
The American Call Option 81
Chapter 12
Forward Rate 85
Chapter 13
Swaps and the Swap Rate 91
The Floating Leg 92
The Swap Rate 93
Swap Rates and Forward Prices 95
Chapter 14
Natural Time Lag and the Convexity Adjustment 97
Chapter 15 Swaption Price 99
Chapter 16 Volatility and Hedging 101
Volatility 101
Hedging 103
The Greeks 104
PART THREE MODEL PRICES
Chapter 17 Option Prices in the Log Normal Case 111
The Option Price Formula 111
Derivation of the Formula 112
Another Proof of the Formula 115
viii Contents
Chapter 18 The Black Scholes Model 117
Derivation of the Black Scholes Formula 118
The Black Scholes Stochastic Differential Equation 121
Black Scholes Parameters 122
Chapter 19 __
The State Space and Evolution 125
The State Space 125
Markov Evolution of Market States 126
Green s Functions for Markov Models 128
Green s Functions and Feynman Kac 129
Chapter 20
Gaussian Models 135
The Model Fundamentals 135
One Factor Gaussian Model 137
Multifactor Gaussian Model 141
Volatility and Correlations 144
Convexity Adjustment 148
Chapter 21
The x2 Model 151
Model Fundamentals 151
Green s Functions 153
The Forward Green s Function 154
The Nondiscounted Green s Function 155
The Shifted Green s Function 156
Chapter 22
Derivation of Green s Functions 159
The One Factor Gaussian Model 163
The Forward Green s Function 163
The Nondiscounted Green s Function 167
The Green s Function Gshifted 167
Contents ix
One Factor Chi Squared Cox Ingersoll Ross Model 169
The Multifactor Gauss Model 176
PART FOUR MATHEMATICAL TOOLS
Chapter 23 Elements of Measure and Integration 185
Measures, Sigma Algebras, Functions 185
Integration 189
Interchanging Limit and Integration 191
Generated a Algebras 191
Product Spaces and Fubini s Theorem 194
Complex Measures 195
The Radon Nikodym Theorem 196
The Distribution Measure 197
Lebesgue Measure and Some Integrals 198
The n k Theorem and Uniqueness of Measures 200
Chapter 24
Probability Theory 201
The Framework 201
cr Algebras 204
Independence 205
Independence and a Algebras 206
Conditional Expectations 207
The Characteristic Function 211
Recovering Q from its Characteristic Function 213
Convergence Notions 215
Chapter 25 Stochastic Processes 219
Some Basic Notions 219
Processes and Filtrations: The Usual Conditions 220
Martingales 221
x Contents
Construction of Stochastic Processes 222
Brownian Motion 226
Markov Processes 229
The Stochastic Integral 232
The Algebra of Stochastic Differentials 232
Chapter 26
Probability and Differential Equations 237
The SDE and the PDE 238
Discretizing the PDE: A Numerical Scheme 240
The Difference Scheme: A Probabilistic Interpretation 243
From the Difference Scheme to the SDE 246
Chapter 27
The Hahn Banach Theorem 249
The Geometric Setting 249
The Algebraic Formulation 251
The Hahn Banach Theorem 255
A Geometric Interpretation 259
END NOTES 263
BIBLIOGRAPHY 269
INDEX 273
LIST OF TABLES 6.1 A Formal Market Model 33
11.1 Google Call Options at 9:17am ET on September 17, 2004, with
Expiration December 17, 2004. Stock Price: .49. 69
11.2 Google Call Options, with strike , at 9:17am ET on
September 17, 2004. Stock Price: .49. 71
11.3 Google September Call Options on Expiration Date September
17, 2004. Stock Price: .49. 72
16.1 Summary of General Price Formulas I 106
16.2 Summary of General Price Formulas II 108
19.1 Green s Functions and Numeraires 129
19.2 Summary of Modeling Concepts 133
20.1 Summary of Gaussian Models 150
22.1 Properties of the Gaussian and x2 Distributions 182
25.1 Ito Multiplication Table 234
xi
|
| adam_txt |
CONTENTS LIST OF TABLES xi
PREFACE xiii
PART ONE FUNDAMENTALS
Chapter 1
Price and Probability 3
An Option Pricing Formula 5
Chapter 2
The Market Equilibrium Measure 9
Chapter 3
Price as Expectation 13
Chapter 4
Changing Numeraires 15
Chapter 5
Changing Numeraires: Examples 19
Fixed Exchange Rate 19
The Log Normal Case 20
Chapter 6 No Arbitrage and the Min Max Argument 23
No Arbitrage and the Pricing Measure 24
Proof of Theorem 6.1.1 26
V
vi Contents
Uniqueness I'Nonuniqueness of the Measure Q 29
The Central Idea: The Max Min Argument 30
A Formal Framework 30
Chapter 7
Conditional Price as Conditional Expectation: The
Martingale Principle 39
Conditional Probabilities and Expectations 39
The Generalized Martingale Principle 41
The Discounted Price Process as a Martingale 41
Change of Numeraire Revisited 43
PART TWO
PRICES OF BASIC INSTRUMENTS
Chapter 8
Bonds and Interest 47
Zero Coupon Default Free Bond Prices 48
Assets with Default Risk 50
Credit Default Swaps: CDS 53
Chapter 9
Forward Prices 55
Chapter 10
Futures Prices 61
The Futures Agreement 62
Futures Prices in the Discrete Case 62
Futures Prices in the Continuous Case 63
Chapter 11
Calls and Puts 67
Options: A Closer Look 69
Call Price 72
Contents vii
Put Price 75
Put Call Parity 76
Another Proof of the Option Price Formula 76
Option Price Inequalities 77
The American Call Option 81
Chapter 12
Forward Rate 85
Chapter 13
Swaps and the Swap Rate 91
The Floating Leg 92
The Swap Rate 93
Swap Rates and Forward Prices 95
Chapter 14
Natural Time Lag and the Convexity Adjustment 97
Chapter 15 Swaption Price 99
Chapter 16 Volatility and Hedging 101
Volatility 101
Hedging 103
"The Greeks" 104
PART THREE MODEL PRICES
Chapter 17 Option Prices in the Log Normal Case 111
The Option Price Formula 111
Derivation of the Formula 112
Another Proof of the Formula 115
viii Contents
Chapter 18 The Black Scholes Model 117
Derivation of the Black Scholes Formula 118
The Black Scholes Stochastic Differential Equation 121
Black Scholes Parameters 122
Chapter 19 _
The State Space and Evolution 125
The State Space 125
Markov Evolution of Market States 126
Green's Functions for Markov Models 128
Green's Functions and Feynman Kac 129
Chapter 20
Gaussian Models 135
The Model Fundamentals 135
One Factor Gaussian Model 137
Multifactor Gaussian Model 141
Volatility and Correlations 144
Convexity Adjustment 148
Chapter 21
The x2 Model 151
Model Fundamentals 151
Green's Functions 153
The Forward Green's Function 154
The Nondiscounted Green's Function 155
The Shifted Green's Function 156
Chapter 22
Derivation of Green's Functions 159
The One Factor Gaussian Model 163
The Forward Green's Function 163
The Nondiscounted Green's Function 167
The Green's Function Gshifted 167
Contents ix
One Factor Chi Squared Cox Ingersoll Ross Model 169
The Multifactor Gauss Model 176
PART FOUR MATHEMATICAL TOOLS
Chapter 23 Elements of Measure and Integration 185
Measures, Sigma Algebras, Functions 185
Integration 189
Interchanging Limit and Integration 191
Generated a Algebras 191
Product Spaces and Fubini's Theorem 194
Complex Measures 195
The Radon Nikodym Theorem 196
The Distribution Measure 197
Lebesgue Measure and Some Integrals 198
The n k Theorem and Uniqueness of Measures 200
Chapter 24
Probability Theory 201
The Framework 201
cr Algebras 204
Independence 205
Independence and a Algebras 206
Conditional Expectations 207
The Characteristic Function 211
Recovering Q from its Characteristic Function 213
Convergence Notions 215
Chapter 25 Stochastic Processes 219
Some Basic Notions 219
Processes and Filtrations: The Usual Conditions 220
Martingales 221
x Contents
Construction of Stochastic Processes 222
Brownian Motion 226
Markov Processes 229
The Stochastic Integral 232
The Algebra of Stochastic Differentials 232
Chapter 26
Probability and Differential Equations 237
The SDE and the PDE 238
Discretizing the PDE: A Numerical Scheme 240
The Difference Scheme: A Probabilistic Interpretation 243
From the Difference Scheme to the SDE 246
Chapter 27
The Hahn Banach Theorem 249
The Geometric Setting 249
The Algebraic Formulation 251
The Hahn Banach Theorem 255
A Geometric Interpretation 259
END NOTES 263
BIBLIOGRAPHY 269
INDEX 273
LIST OF TABLES 6.1 A Formal Market Model 33
11.1 Google Call Options at 9:17am ET on September 17, 2004, with
Expiration December 17, 2004. Stock Price: \.49. 69
11.2 Google Call Options, with strike \, at 9:17am ET on
September 17, 2004. Stock Price: \.49. 71
11.3 Google September Call Options on Expiration Date September
17, 2004. Stock Price: \.49. 72
16.1 Summary of General Price Formulas I 106
16.2 Summary of General Price Formulas II 108
19.1 Green's Functions and Numeraires 129
19.2 Summary of Modeling Concepts 133
20.1 Summary of Gaussian Models 150
22.1 Properties of the Gaussian and x2 Distributions 182
25.1 Ito Multiplication Table 234
xi |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:09:07Z |
| indexdate | 2024-07-09T20:41:19Z |
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| isbn | 0071445889 |
| language | English |
| lccn | 2004028196 |
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| series2 | The McGraw-Hill library of investment and finance |
| spelling | Sengupta, Ambar 1963- Verfasser (DE-588)120724952 aut Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives Ambar N. Sengupta New York [u.a.] McGraw-Hill c2005 xiv, 282 p. 24 cm txt rdacontent n rdamedia nc rdacarrier The McGraw-Hill library of investment and finance Includes bibliographical references (p. 269-271) and index Irwin Library of Investment and Finance Pricing Derivatives provides investors with a clear understanding of derivative pricing models by first focusing on the underlying mathematics and financial concepts upon which the models were originally built. Trading consultant Professor Ambar Sengupta uses short, to-the-point chapters to examine the relation between price and probability as well as pricing structures of all major derivative instruments. Other topics covered include foundations of stochastic models of pricing, along with methods for establishing optimal prices in terms of the max-min principles that underlie game theory. Derivaten (financiën) gtt Prijsberekening gtt Mathematik Derivative securities Prices Mathematics Preisbildung (DE-588)4047103-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Preisbildung (DE-588)4047103-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 http://www.loc.gov/catdir/toc/ecip054/2004028196.html Table of contents http://www.loc.gov/catdir/enhancements/fy0617/2004028196-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0617/2004028196-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014886616&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sengupta, Ambar 1963- Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives Derivaten (financiën) gtt Prijsberekening gtt Mathematik Derivative securities Prices Mathematics Preisbildung (DE-588)4047103-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd |
| subject_GND | (DE-588)4047103-2 (DE-588)4114528-8 (DE-588)4381572-8 |
| title | Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives |
| title_auth | Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives |
| title_exact_search | Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives |
| title_exact_search_txtP | Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives |
| title_full | Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives Ambar N. Sengupta |
| title_fullStr | Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives Ambar N. Sengupta |
| title_full_unstemmed | Pricing derivatives the financial concepts underlying the mathematics of pricing derivatives Ambar N. Sengupta |
| title_short | Pricing derivatives |
| title_sort | pricing derivatives the financial concepts underlying the mathematics of pricing derivatives |
| title_sub | the financial concepts underlying the mathematics of pricing derivatives |
| topic | Derivaten (financiën) gtt Prijsberekening gtt Mathematik Derivative securities Prices Mathematics Preisbildung (DE-588)4047103-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd |
| topic_facet | Derivaten (financiën) Prijsberekening Mathematik Derivative securities Prices Mathematics Preisbildung Mathematisches Modell Derivat Wertpapier |
| url | http://www.loc.gov/catdir/toc/ecip054/2004028196.html http://www.loc.gov/catdir/enhancements/fy0617/2004028196-b.html http://www.loc.gov/catdir/enhancements/fy0617/2004028196-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014886616&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT senguptaambar pricingderivativesthefinancialconceptsunderlyingthemathematicsofpricingderivatives |