Financial geometry: a geometric approach to hedging and risk management
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Financial Times/Prentice Hall
2003
|
| Schriftenreihe: | Professional financial series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXVI, 381 S. graph. Darst. 25 cm |
| ISBN: | 0273661965 |
Internformat
MARC
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| 100 | 1 | |a Kuruc, Alvin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Financial geometry |b a geometric approach to hedging and risk management |c Alvin Kuruc |
| 264 | 1 | |a New York |b Financial Times/Prentice Hall |c 2003 | |
| 300 | |a XXVI, 381 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Professional financial series | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Hedging (Finance) | |
| 650 | 4 | |a Risk management | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016848656&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016848656 | ||
Datensatz im Suchindex
| _version_ | 1804138173082632192 |
|---|---|
| adam_text | Contents
Foreword xvii
Preface xxi
Acknowledgements xxv
Prologue 1
PART I
Foundations
1 Marking to market 7
1.1 Mark to market 7
1.2 On-market and off-market instruments 8
1.2.1 Types of financial markets 9
1.2.2 Key instrument distinctions 10
1.2.3 On-market instruments 11
1.2.4 Off-market instruments 12
1.3 Units of account 14
1.3.1 Accounting currencies 14
1.3-2 Currency conversion 14
1.4 Accounting versus risk management 16
1.4.1 Reporting frequency 17
1.4.2 Past versus future orientation 17
1.4.3 Probabilistic modelling requirements 17
1.4.4 Liquidity and funding risks 17
1.4.5 Specific accounting requirements 18
1.4.6 Modelling uncertainty 18
1.5 Notes and references 18
2 Valuation techniques 19
2.1 Asset-value notation 19
.... vii ••¦•
PRELIMS
2.2 Future cash flows 21
2.2.1 Cash rates 21
2.2.2 Interpolation 24
2.3 Forward contracts 26
2.4 Interest-rate swaps 28
2.4.1 Par swaps 28
2.4.2 Off-market swaps 31
2.5 Calls and puts 33
2.5.1 Option-pricing theory 33
2.5.2 Black-Scholes model 35
2.5.3 Black-Scholes volatility surface 36
2.6 General options 37
2.7 Notes and references 39
3 Introduction to risk management 40
3.1 Market-state space and risk factors 40
3.1.1 Market-state space 40
3.1.2 Risk factors 41
3.1.3 Coordinate systems 41
3.1.4 Valuation functions 43
3.1.5 Example: zero-coupon valuation 45
3.1.6 Alternative coordinate systems 47
3.1.7 Observables 47
3.1.8 Types of risk factors 48
32 Risk-management techniques 48
3.2.1 Mark-to-market 49
3-2.2 Sensitivity analysis 49
3-2.3 Scenario analysis 51
3-2.4 Value-at-risk analysis 53
3.2.5 What are we missing? 54
3-3 The devil is in the details 55
3.4 Notes and references 56
4 Classical bond geometry 57
4.1 Bonds 58
4.2 Risk factors for bonds 58
4.2.1 Price 58
4.2.2 Yield to maturity 59
4.2.3 Arbitrage restrictions 61
.... viii ¦¦••
Contents
4.2.4 Coordinate maps 61
4.3 Valuation functions 63
4.4 Reconciling risk factors 65
4.5 Sensitivities 66
4.5.1 Differentiation of univariate functions 66
4.5.2 Univariate chain rule 67
4.5.3 First-order sensitivities 68
4.5.4 Second-order sensitivities 69
4.6 Tangent vectors and differentials 70
4.6.1 Path derivatives 71
4.6.2 Tangent vectors 73
4.6.3 Differentials 76
4.7 Reconciling sensitivities 78
4.7.1 Tangent vectors 79
4.7.2 Differentials 80
4.8 Classical sensitivities 82
4.8.1 Ten-year equivalents 82
4.8.2 Modified duration 82
4.8.3 Macaulay duration 83
4.8.4 Dollar duration 84
4.8.5 Convexity 84
4.9 Commensurability 85
4.10 Notes and references 85
5 Modern bond geometry 86
5.1 Time value of money 86
5.1.1 Absolute and relative dates 87
5.1.2 Nominal and actual terms 87
5.1.3 Credit quality 87
5.2 Risk factors 87
5.2.1 Zero-coupon discount factors 88
5.2.2 Log discount factors 89
5.2.3 Zero-coupon discount rates 91
5.2.4 Forward discount factors 93
5.2.5 Forward rates 93
5.2.6 Par rates 94
5.2.7 Market risk factors 95
5.3 Valuation functions 97
5.4 Sensitivities 99
.... jx ....
PRELIMS
5.4.1 Differentiation of multivariate functions 99
5.4.2 Multivariate chain rule 101
5.4.3 Sensitivities to discount factors 102
5.4.4 Sensitivities to log discount factors 102
5.4.5 Sensitivities to zero rates 102
5.4.6 Sensitivities to forward discount factors 103
5.4.7 Sensitivities to forward rates 103
5.4.8 Sensitivities to par rates 103
5.4.9 Market sensitivities 104
5.5 Tangent vectors and differentials 105
5.5.1 Tangent vectors 105
5.5.2 Differentials 109
5.6 Reconciling sensitivities HI
5.6.1 Tangent vectors HI
5.6.2 Differentials 114
5.7 Notes and references 115
PART II
Asset values
6 Interpolation 119
6.1 Introduction 119
6.2 Risk factors 120
6.2.1 Entire term structure 120
6.2.2 Key term structure 121
6.3 Valuation functions 124
6.3.1 Entire term structure 124
6.3.2 Key term structure 124
6.4 Sensitivities 127
6.4.1 Entire term structure 127
6.4.2 Key term structure 127
6.5 Perturbations 130
6.5.1 Entire term structure 130
6.5.2 Key term structure 130
6.6 Differentials 133
6.7 Bucketing 133
6.8 Notes and references 136
¦-X--
Contents
7 Interest-rate hedging 137
7.1 Introduction to hedging 137
7.2 Delta hedging 138
7.2.1 Basic theory 138
7.2.2 Duration hedging 139
7.2.3 Cash-flow hedging 141
7.2.4 Curve hedging 142
7.3 Subspace hedging 144
7.4 Weighted hedging 147
7.5 Notes and references 148
8 Foreign-currency geometry 149
8.1 Foreign exchange 150
8.1.1 Market description 150
8.1.2 Systematic description 151
8.1.3 No-arbitrage relations 151
8.2 Risk factors 152
8.2.1 Exchange rates 152
8.2.2 Log foreign-exchange rates 156
8.3 Valuation functions 157
8.4 Sensitivities 160
8.4.1 Exchange rates 160
8.4.2 Log exchange rates 161
8.5 Reconciling sensitivities 165
8.5.1 Perturbations 165
8.5.2 Differentials 167
8.6 Change of base currency 168
8.6.1 Asset values 168
8.6.2 Log asset values 169
8.7 Notes and references 170
9 Demand-deposit geometry 171
9.1 Introduction 171
9.2 Risk factors 172
9.2.1 Asset-value manifold 172
9.2.2 Asset values 174
9-2.3 Relation to foreign-exchange rates 175
9.3 Valuation functions 176
9.3.1 Abstract valuation space 176
.... xi....
PRELIMS
9.3.2 Valuation of demand deposits 177
9.3.3 Relation to foreign-exchange rates 179
9.4 Sensitivities I81
9.5 Relationship to foreign-exchange sensitivities 183
9.5.1 Perturbations 184
9.5.2 Differentials 187
9.5.3 Application 189
9-6 Notes and references 191
10 Asset-value geometry 192
10.1 Asset values 192
10.2 Risk factors 193
10.2.1 Absolute asset values 193
10.2.2 Relative asset values 19o
10.3 Valuation functions 198
10.3.1 Abstract asset values 198
10.3.2 Absolute asset values 199
10.33 Relative asset values 199
10.3-4 Foreign-exchange rates and discount factors 200
10.4 Sensitivities 200
10.4.1 Abstract asset values 200
10.4.2 Absolute asset values 202
10.4.3 Log absolute asset values 202
10.4.4 Relative asset values 202
10.4.5 Log relative asset values 202
10.5 Implementation 203
10.5.1 Bucketing 203
10.5.2 Implementation by asset value and discount-factor perturbations 206
10.6 Notes and references 207
PART III
Metrics
11 Value at risk 211
11.1 Value-at-risk methodologies 211
11.2 Probabilistic model 212
11.3 Geometrical interpretation 214
.... xii ¦¦¦¦
Contents
11.31 Length and angle 215
11.3.2 Change of coordinates 219
11.4 Change of base currency 221
11.5 Benchmarking 223
11.6 Notes and references 227
12 Risk-factor mapping 228
12.1 Natural and modelled risk factors 228
12.2 Perturbations and differentials 229
12.3 Covariance structure 230
12.4 Mapping term structures 231
12.4.1 Asset series 231
12.4.2 Factor-name association 232
12.4.3 Factor substitution and scaling 234
12.5 Mapping stocks 236
12.5.1 Beta 236
12.5.2 Native currency 237
12.6 Notes and references 239
13 Risk contributions 240
13.1 Basic theory 240
13.2 Variance/covariance results 243
13-3 Limiting cases 244
13-31 Uncorrelated instruments 244
133-2 Perfectly correlated instruments 245
13-4 Notes and references 245
14 Variance/covariance hedging 246
14.1 Motivation 246
14.2 Implementation 247
14.3 Application 250
14.4 Notes and references 251
PART IV
Implied volatility
15 Option geometry 255
.... xjij ....
PRELIMS
15.1 Stock options 255
15.2 Risk factors 256
15.2.1 Market prices 256
15.2.2 Black-Scholes model 257
15.2.3 Bachelier model 26l
15.2.4 Model inconsistency -263
15.3 Valuation functions 263
15.3.1 Market-price coordinate system 263
15.3.2 Black-Scholes coordinate system 264
15.3.3 Bachelier coordinate system 265
15.4 Sensitivities 265
15.4.1 Market-price coordinate system 265
15.4.2 Black-Scholes coordinate system 266
15.4.3 Bachelier coordinate system 268
15.5 Reconciling sensitivities 269
15.5.1 Perturbations 269
15.5.2 Differentials 272
15.6 Valuing other instruments 272
15.7 Profit and loss attribution 273
15.8 Notes and references 276
16 Volatility curves 277
16.1 Market-state space 277
16.2 Risk factors 278
16.2.1 Call prices 278
16.2.2 Black-Scholes volatility curve 282
16.2.3 Bull-option prices 283
16.2.4 Arrow-Debreu prices 28o
16.3 Valuation functions 289
16.3-1 Arrow-Debreu coordinate system 290
16.3-2 Bull-option coordinate system 291
16.33 Call-price coordinate system 293
16.3.4 Black-Scholes coordinate system 294
16.4 Sensitivities 295
16.4.1 Functional derivatives 295
16.4.2 Call-price coordinate system 295
16.4.3 Bull-option coordinate system 296
16.4.4 Arrow-Debreu coordinate system 297
16.4.5 Black-Scholes coordinate system 298
.... xiv ....
Contents
16.5 Reconciling sensitivities 301
16.6 Notes and references 303
17 Volatility surfaces 304
17.1 Market-state space 304
17.2 Risk factors 305
17.2.1 Call prices 305
17.2.2 Black-Scholes volatility surface 307
17.2.3 Local-volatility surface 308
17.2.4 Arrow-Debreu price surface 309
17.3 Valuation functions 311
17.31 Arrow-Debreu coordinate system 311
17.3-2 Call-price coordinate system 312
17.3-3 Black-Scholes coordinate system 313
17.3-4 Local-volatility coordinate system 313
17.4 Sensitivities 313
17.4.1 Functional derivatives 313
17.4.2 Call prices 314
17.4.3 Arrow-Debreu prices 315
17.4.4 Black-Scholes coordinate system 316
17.5 Reconciling sensitivities 319
17.6 Notes and references 319
18 Valuation models 320
18.1 Market-state spaces 321
18.2 Risk factors 322
18.2.1 Risk-neutral models 322
18.2.2 Parameterized valuation models 323
18.3 Valuation functions 326
18.3-1 Risk-neutral valuation models 326
18.3-2 Parameterized valuation models 327
18.3-3 Calibration procedures 328
18.4 Sensitivities 330
18.4.1 Parameterized model sensitivities 330
18.4.2 European option prices 331
18.5 Notes and references 332
Epilogue 333
.... xv....
PRELIMS
A The dimension of time 334
A.I Time concepts 334
A. 2 Choice of time horizon 336
A.2.1 Present valuation functions 337
A.2.2 Future valuation functions 338
A.2.3 Practical considerations 339
A.3 Notes and references 341
B Black-Scholes and Bachelier calculations 342
B.I Valuation functions 342
B.I.I Black-Scholes model 342
B.I.2 Bachelier model 344
B.2 Sensitivities 345
B.2.1 Black-Scholes model 345
B.2.2 Bachelier model 353
C Index of notation 355
C.I Symbols 355
C.2 Roman, bold and italic 356
C.2.1 Lower case 356
C.2.2 Upper case 360
C3 Blackboard bold 361
C.4 Fraktur 362
C.4.1 Lowercase 362
C.4.2 Upper case 363
C5 Sans serif 363
C.6 Greek 363
C.6.1 Lower case 363
C.6.2 Upper case 366
References 367
Index 369
.... xvi...
|
| adam_txt |
Contents
Foreword xvii
Preface xxi
Acknowledgements xxv
Prologue 1
PART I
Foundations
1 Marking to market 7
1.1 Mark to market 7
1.2 On-market and off-market instruments 8
1.2.1 Types of financial markets 9
1.2.2 Key instrument distinctions 10
1.2.3 On-market instruments 11
1.2.4 Off-market instruments 12
1.3 Units of account 14
1.3.1 Accounting currencies 14
1.3-2 Currency conversion 14
1.4 Accounting versus risk management 16
1.4.1 Reporting frequency 17
1.4.2 Past versus future orientation 17
1.4.3 Probabilistic modelling requirements 17
1.4.4 Liquidity and funding risks 17
1.4.5 Specific accounting requirements 18
1.4.6 Modelling uncertainty 18
1.5 Notes and references 18
2 Valuation techniques 19
2.1 Asset-value notation 19
. vii ••¦•
PRELIMS
2.2 Future cash flows 21
2.2.1 Cash rates 21
2.2.2 Interpolation 24
2.3 Forward contracts 26
2.4 Interest-rate swaps 28
2.4.1 Par swaps 28
2.4.2 Off-market swaps 31
2.5 Calls and puts 33
2.5.1 Option-pricing theory 33
2.5.2 Black-Scholes model 35
2.5.3 Black-Scholes volatility surface 36
2.6 General options 37
2.7 Notes and references 39
3 Introduction to risk management 40
3.1 Market-state space and risk factors 40
3.1.1 Market-state space 40
3.1.2 Risk factors 41
3.1.3 Coordinate systems 41
3.1.4 Valuation functions 43
3.1.5 Example: zero-coupon valuation 45
3.1.6 Alternative coordinate systems 47
3.1.7 Observables 47
3.1.8 Types of risk factors 48
32 Risk-management techniques 48
3.2.1 Mark-to-market 49
3-2.2 Sensitivity analysis 49
3-2.3 Scenario analysis 51
3-2.4 Value-at-risk analysis 53
3.2.5 What are we missing? 54
3-3 The devil is in the details 55
3.4 Notes and references 56
4 Classical bond geometry 57
4.1 Bonds 58
4.2 Risk factors for bonds 58
4.2.1 Price 58
4.2.2 Yield to maturity 59
4.2.3 Arbitrage restrictions 61
. viii ¦¦••
Contents
4.2.4 Coordinate maps 61
4.3 Valuation functions 63
4.4 Reconciling risk factors 65
4.5 Sensitivities 66
4.5.1 Differentiation of univariate functions 66
4.5.2 Univariate chain rule 67
4.5.3 First-order sensitivities 68
4.5.4 Second-order sensitivities 69
4.6 Tangent vectors and differentials 70
4.6.1 Path derivatives 71
4.6.2 Tangent vectors 73
4.6.3 Differentials 76
4.7 Reconciling sensitivities 78
4.7.1 Tangent vectors 79
4.7.2 Differentials 80
4.8 Classical sensitivities 82
4.8.1 Ten-year equivalents 82
4.8.2 Modified duration 82
4.8.3 Macaulay duration 83
4.8.4 Dollar duration 84
4.8.5 Convexity 84
4.9 Commensurability 85
4.10 Notes and references 85
5 Modern bond geometry 86
5.1 Time value of money 86
5.1.1 Absolute and relative dates 87
5.1.2 Nominal and actual terms 87
5.1.3 Credit quality 87
5.2 Risk factors 87
5.2.1 Zero-coupon discount factors 88
5.2.2 Log discount factors 89
5.2.3 Zero-coupon discount rates 91
5.2.4 Forward discount factors 93
5.2.5 Forward rates 93
5.2.6 Par rates 94
5.2.7 'Market' risk factors 95
5.3 Valuation functions 97
5.4 Sensitivities 99
. jx .
PRELIMS
5.4.1 Differentiation of multivariate functions 99
5.4.2 Multivariate chain rule 101
5.4.3 Sensitivities to discount factors 102
5.4.4 Sensitivities to log discount factors 102
5.4.5 Sensitivities to zero rates 102
5.4.6 Sensitivities to forward discount factors 103
5.4.7 Sensitivities to forward rates 103
5.4.8 Sensitivities to par rates 103
5.4.9 'Market' sensitivities 104
5.5 Tangent vectors and differentials 105
5.5.1 Tangent vectors 105
5.5.2 Differentials 109
5.6 Reconciling sensitivities HI
5.6.1 Tangent vectors HI
5.6.2 Differentials 114
5.7 Notes and references 115
PART II
Asset values
6 Interpolation 119
6.1 Introduction 119
6.2 Risk factors 120
6.2.1 Entire term structure 120
6.2.2 Key term structure 121
6.3 Valuation functions 124
6.3.1 Entire term structure 124
6.3.2 Key term structure 124
6.4 Sensitivities 127
6.4.1 Entire term structure 127
6.4.2 Key term structure 127
6.5 Perturbations 130
6.5.1 Entire term structure 130
6.5.2 Key term structure 130
6.6 Differentials 133
6.7 Bucketing 133
6.8 Notes and references 136
¦-X--
Contents
7 Interest-rate hedging 137
7.1 Introduction to hedging 137
7.2 Delta hedging 138
7.2.1 Basic theory 138
7.2.2 Duration hedging 139
7.2.3 Cash-flow hedging 141
7.2.4 Curve hedging 142
7.3 Subspace hedging 144
7.4 Weighted hedging 147
7.5 Notes and references 148
8 Foreign-currency geometry 149
8.1 Foreign exchange 150
8.1.1 Market description 150
8.1.2 Systematic description 151
8.1.3 No-arbitrage relations 151
8.2 Risk factors 152
8.2.1 Exchange rates 152
8.2.2 Log foreign-exchange rates 156
8.3 Valuation functions 157
8.4 Sensitivities 160
8.4.1 Exchange rates 160
8.4.2 Log exchange rates 161
8.5 Reconciling sensitivities 165
8.5.1 Perturbations 165
8.5.2 Differentials 167
8.6 Change of base currency 168
8.6.1 Asset values 168
8.6.2 Log asset values 169
8.7 Notes and references 170
9 Demand-deposit geometry 171
9.1 Introduction 171
9.2 Risk factors 172
9.2.1 Asset-value manifold 172
9.2.2 Asset values 174
9-2.3 Relation to foreign-exchange rates 175
9.3 Valuation functions 176
9.3.1 Abstract valuation space 176
. xi.
PRELIMS
9.3.2 Valuation of demand deposits 177
9.3.3 Relation to foreign-exchange rates 179
9.4 Sensitivities I81
9.5 Relationship to foreign-exchange sensitivities 183
9.5.1 Perturbations 184
9.5.2 Differentials 187
9.5.3 Application 189
9-6 Notes and references 191
10 Asset-value geometry 192
10.1 Asset values 192
10.2 Risk factors 193
10.2.1 Absolute asset values 193
10.2.2 Relative asset values 19o
10.3 Valuation functions 198
10.3.1 Abstract asset values 198
10.3.2 Absolute asset values 199
10.33 Relative asset values 199
10.3-4 Foreign-exchange rates and discount factors 200
10.4 Sensitivities 200
10.4.1 Abstract asset values 200
10.4.2 Absolute asset values 202
10.4.3 Log absolute asset values 202
10.4.4 Relative asset values 202
10.4.5 Log relative asset values 202
10.5 Implementation 203
10.5.1 Bucketing 203
10.5.2 Implementation by asset value and discount-factor perturbations 206
10.6 Notes and references 207
PART III
Metrics
11 Value at risk 211
11.1 Value-at-risk methodologies 211
11.2 Probabilistic model 212
11.3 Geometrical interpretation 214
. xii ¦¦¦¦
Contents
11.31 Length and angle 215
11.3.2 Change of coordinates 219
11.4 Change of base currency 221
11.5 Benchmarking 223
11.6 Notes and references 227
12 Risk-factor mapping 228
12.1 Natural and modelled risk factors 228
12.2 Perturbations and differentials 229
12.3 Covariance structure 230
12.4 Mapping term structures 231
12.4.1 Asset series 231
12.4.2 Factor-name association 232
12.4.3 Factor substitution and scaling 234
12.5 Mapping stocks 236
12.5.1 Beta 236
12.5.2 Native currency 237
12.6 Notes and references 239
13 Risk contributions 240
13.1 Basic theory 240
13.2 Variance/covariance results 243
13-3 Limiting cases 244
13-31 Uncorrelated instruments 244
133-2 Perfectly correlated instruments 245
13-4 Notes and references 245
14 Variance/covariance hedging 246
14.1 Motivation 246
14.2 Implementation 247
14.3 Application 250
14.4 Notes and references 251
PART IV
Implied volatility
15 Option geometry 255
. xjij .
PRELIMS
15.1 Stock options 255
15.2 Risk factors 256
15.2.1 Market prices 256
15.2.2 Black-Scholes model 257
15.2.3 Bachelier model 26l
15.2.4 Model inconsistency -263
15.3 Valuation functions 263
15.3.1 Market-price coordinate system 263
15.3.2 Black-Scholes coordinate system 264
15.3.3 Bachelier coordinate system 265
15.4 Sensitivities 265
15.4.1 Market-price coordinate system 265
15.4.2 Black-Scholes coordinate system 266
15.4.3 Bachelier coordinate system 268
15.5 Reconciling sensitivities 269
15.5.1 Perturbations 269
15.5.2 Differentials 272
15.6 Valuing other instruments 272
15.7 Profit and loss attribution 273
15.8 Notes and references 276
16 Volatility curves 277
16.1 Market-state space 277
16.2 Risk factors 278
16.2.1 Call prices 278
16.2.2 Black-Scholes volatility curve 282
16.2.3 Bull-option prices 283
16.2.4 Arrow-Debreu prices 28o
16.3 Valuation functions 289
16.3-1 Arrow-Debreu coordinate system 290
16.3-2 Bull-option coordinate system 291
16.33 Call-price coordinate system 293
16.3.4 Black-Scholes coordinate system 294
16.4 Sensitivities 295
16.4.1 Functional derivatives 295
16.4.2 Call-price coordinate system 295
16.4.3 Bull-option coordinate system 296
16.4.4 Arrow-Debreu coordinate system 297
16.4.5 Black-Scholes coordinate system 298
. xiv .
Contents
16.5 Reconciling sensitivities 301
16.6 Notes and references 303
17 Volatility surfaces 304
17.1 Market-state space 304
17.2 Risk factors 305
17.2.1 Call prices 305
17.2.2 Black-Scholes volatility surface 307
17.2.3 Local-volatility surface 308
17.2.4 Arrow-Debreu price surface 309
17.3 Valuation functions 311
17.31 Arrow-Debreu coordinate system 311
17.3-2 Call-price coordinate system 312
17.3-3 Black-Scholes coordinate system 313
17.3-4 Local-volatility coordinate system 313
17.4 Sensitivities 313
17.4.1 Functional derivatives 313
17.4.2 Call prices 314
17.4.3 Arrow-Debreu prices 315
17.4.4 Black-Scholes coordinate system 316
17.5 Reconciling sensitivities 319
17.6 Notes and references 319
18 Valuation models 320
18.1 Market-state spaces 321
18.2 Risk factors 322
18.2.1 Risk-neutral models 322
18.2.2 Parameterized valuation models 323
18.3 Valuation functions 326
18.3-1 Risk-neutral valuation models 326
18.3-2 Parameterized valuation models 327
18.3-3 Calibration procedures 328
18.4 Sensitivities 330
18.4.1 Parameterized model sensitivities 330
18.4.2 European option prices 331
18.5 Notes and references 332
Epilogue 333
. xv.
PRELIMS
A The dimension of time 334
A.I Time concepts 334
A. 2 Choice of time horizon 336
A.2.1 Present valuation functions 337
A.2.2 Future valuation functions 338
A.2.3 Practical considerations 339
A.3 Notes and references 341
B Black-Scholes and Bachelier calculations 342
B.I Valuation functions 342
B.I.I Black-Scholes model 342
B.I.2 Bachelier model 344
B.2 Sensitivities 345
B.2.1 Black-Scholes model 345
B.2.2 Bachelier model 353
C Index of notation 355
C.I Symbols 355
C.2 Roman, bold and italic 356
C.2.1 Lower case 356
C.2.2 Upper case 360
C3 Blackboard bold 361
C.4 Fraktur 362
C.4.1 Lowercase 362
C.4.2 Upper case 363
C5 Sans serif 363
C.6 Greek 363
C.6.1 Lower case 363
C.6.2 Upper case 366
References 367
Index 369
. xvi. |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:34:29Z |
| indexdate | 2024-07-09T21:23:58Z |
| institution | BVB |
| isbn | 0273661965 |
| language | English |
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| spelling | Kuruc, Alvin Verfasser aut Financial geometry a geometric approach to hedging and risk management Alvin Kuruc New York Financial Times/Prentice Hall 2003 XXVI, 381 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Professional financial series Includes bibliographical references and index Hedging (Finance) Risk management HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016848656&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuruc, Alvin Financial geometry a geometric approach to hedging and risk management Hedging (Finance) Risk management |
| title | Financial geometry a geometric approach to hedging and risk management |
| title_auth | Financial geometry a geometric approach to hedging and risk management |
| title_exact_search | Financial geometry a geometric approach to hedging and risk management |
| title_exact_search_txtP | Financial geometry a geometric approach to hedging and risk management |
| title_full | Financial geometry a geometric approach to hedging and risk management Alvin Kuruc |
| title_fullStr | Financial geometry a geometric approach to hedging and risk management Alvin Kuruc |
| title_full_unstemmed | Financial geometry a geometric approach to hedging and risk management Alvin Kuruc |
| title_short | Financial geometry |
| title_sort | financial geometry a geometric approach to hedging and risk management |
| title_sub | a geometric approach to hedging and risk management |
| topic | Hedging (Finance) Risk management |
| topic_facet | Hedging (Finance) Risk management |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016848656&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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