The art of quantitative finance: Vol. 2 Volatilities, stochastic analysis and valuation tools
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| Format: | Buch |
| Sprache: | English |
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Cham
Springer
[2023]
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 353 Seiten Diagramme |
| ISBN: | 9783031238697 |
Internformat
MARC
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| 245 | 1 | 0 | |a The art of quantitative finance |n Vol. 2 |p Volatilities, stochastic analysis and valuation tools |c Gerhard Larcher |
| 264 | 1 | |a Cham |b Springer |c [2023] | |
| 300 | |a xii, 353 Seiten |b Diagramme | ||
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Datensatz im Suchindex
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| adam_text | Contents 1 Volatilities........................................................................................................ 1.1 Volatility I: Historical Volatility.......................................................... 1.2 Volatility II: ARCH Models................................................................. 1.3 Volatility III: How to Use and Forecast Volatility.............................. 1.4 Volatility IV: Magnitude of the Historical Volatility oftheS P500..................................................................................... 1.5 Volatility V: Volatility in Derivatives Pricing..................................... 1.6 Derivatives Pricing with Time- (and Price-) Dependent Volatility: the Dupire Model............................................................... 1.7 Implied Volatility................................................. .·.............................. 1.8 Implied Volatilities of Call Options and Put Options with Same Expiration and Strike................................................................ 1.9 Volatility Skews, Volatility Smiles, and Volatility Surfaces............ 1.10 Inferences From Implied Volatilities About the Market-Anticipated Distribution of the Underlying Asset’s Price........................................................................................ 1.11 Volatility Indices................................................................................... 1.12 Basic Properties of the VIX................................................................. 1.13 Relation and CorrelationsBetween VIX and
SPX.............................. 1.14 Influence of Price- and/or Time-Dependent Volatility on Delta, Gamma, and Theta................................................................... 1.15 Combined Trading of SPX and VIX for Hedging Purposes............ 1.16 Relation and Correlations of VIX with Historical and Realized Volatility............................................................................... 1.17 The СВОЕ S P500 Put Write Index................................................. 1.18 The VIX Calculation Methodology.................................................... 1.19 The Volatility Weekend Effect........................................................... 1.20 Derivatives on the VIX: VIX Futures................................................. 1.21 VIX Options.......................................................................................... 1.22 Payoff and Profit Functions of a Trading Strategy for Combinations of SPX and VIX Options.............................................. References.......................................................................................................... 1 1 9 14 21 22 25 30 37 38 42 50 54 58 66 70 78 84 86 93 96 106 109 117 ix
Contents x 2 Extensions of the Black-Scholes Theory to Other Types of Options (Futures Options, Currency Options, American Options, Path-Dependent Options, Multi-asset Options)................ 119 Introduction and Discussions So Far .................................................. 119 Currency Options................................................................................... 121 Futures Options...................................................................................... 126 Valuation of American Options and of Bermudan Options Through Backwardation (the Algorithm)................................ 131 2.5 Valuation Examples for American Options in the Binomial and in the Wiener Model.......................................................... 138 2.6 Hedging American Options................................................................... 142 2.7 Path-Dependent (Exotic) Derivatives, Definition and Examples .... 144 2.8 Valuation of Path-Dependent Options, the Black-Scholes Formula for Path-Dependent Options...................................... 150 2.9 Numerical Valuation Example of a Path-Dependent Option in a Three-Step Binomial Model (European and American)........... 155 2.10 The Complexity of Pricing Path-Dependent Options in an N-Step Binomial Model in General and, For Example, for Lookback Options................................................................................ 157 2.11 Valuation of an American Lookback Option in a Four-Step Binomial Model (Numerical Example)................................... 163 2.12 Explicit Formulas for European
Path-Dependent Options, For Example, В airier Options.................................................. 167 2.13 Explicit Formulas for European Path-Dependent Options, For Example, Geometric Asian Options................................. 170 2.14 Brief Comment on Hedging Path-Dependent Derivatives................ 178 2.15 Valuation of Derivatives Using Monte Carlo Methods, Basic Principle..................................................................................... 179 2.16 Valuation of European Path-Dependent Derivatives with Monte Carlo Methods.............................................................. 183 2.17 Monte Carlo Valuation of Asian Options............................................ 184 2.18 Monte Carlo Valuation of Barrier Options......................................... 185 2.19 Barrier Options in Turbo and Bonus Certificates .............................. 189 2.20 Estimating Greeks (Especially Delta and Gamma) of Derivatives with Monte Carlo.................................................. 192 2.21 Estimating Delta and Delta Hedging for Path-Dependent Derivatives (e.g. Geometric Asian Option)............................ 200 2.22 Some Fundamental Remarks on Monte Carlo Methods and on the Convergence of Monte Carlo Methods................................... 207 2.23 Some Remarks on Random Numbers................................................. 212 2.24 A Remark on Quasi-Monte Carlo Methods...................................... 217 2.25 An Example of Low-Discrepancy QMC Point Sets: The Hammersley Point
Sets............................................................ 226 2.26 Variance Reduction Methods for Monte Carlo.................................. 229 2.1 2.2 2.3 2.4
Contents xi Using Monte Carlo with Control Variates to Value an Arithmetic Asian Option......................................................... 233 2.28 Multi-asset Options.............................................................................. 236 2.29 Modelling Correlated Financial Products in the Wiener Model, Cholesky Decomposition........................................... 238 2.30 Valuation of Multi-asset Options......................................................... 242 2.31 Example of Pricing a Multi-asset Option with MC and with QMC.......................................................................... 245 References....................................................................................................... 250 2.27 3 Fundamentals: Stochastic Analysis and Applications, Interest Rate Dynamics, and Basic Principles of Pricing Interest Rate Derivatives................................................................................................ 251 3.1 Modelling of Interest RateDynamics................................................... 252 3.2 Differential Representation of Stochastic Processes: Heuristic Introduction.......................................................................................... 254 3.3 Simulation of Ito Processes andBasic Models................................... 266 3.4 Excursus: The Ito Formula and Differential Notation oftheGBM.............................................................................. 275 3.5 Interest Rate Modelling Using Mean-Reverting Ornstein-
Uhlenbeck................................................................ 279 3.6 Examples of Interest Rate Derivatives and a Principal Methodology for Pricing such Derivatives............................ 285 3.7 Basic Concepts of Frictionless Interest Rate Markets: Zero-Coupon Bonds and Interest Rates.................................. 287 3.8 Fixed and Floating Rate Coupon Bonds............................................. 292 3.9 Interest Rate Swaps............................................................................... 295 3.10 Valuation of Bond Prices and Interest Rate Derivatives in a Short-Rate Approach............................................................... 296 3.11 The Mean-Reverting Vasicek Model and the Hull-White Model for the Short Rate......................................................... 303 3.12 Affine Model Structures of Bond Prices............................................ 304 3.13 Bond Prices in the Vasicek Model and Calibration in the Vasicek Model.......................................................................... 306 3.14 Bond Prices in the Hull-White Model and Calibration in the Hull-White Model................................................................... 308 3.15 Valuation and Put-Call Parity of Call and Put Options on Bond Prices.............................................................................. 311 3.16 Valuation of Caplets and Floorlets (as Well as Interest Rate Caps and Interest Rate Floors)................................................ 312 3.17 The Black-Scholes Differential
Equation........................................... 316 3.18 The Stochastic Ito Integral: Heuristic Explanation and Basic Properties................................................................................... 319 3.19 Conditional Expectations and Martingales........................................ 330 3.20 The Feynman-Kac Formula................................................................ 333
xii Contents 3.21 The Black-Scholes Formula.............................................................. 3.22 The Black-Scholes Model as a Complete Market and Hedging of Derivatives......................................................... 338 3.23 The Multidimensional Black-Scholes Model and Its Completeness............................................................ 341 3.24 Incomplete Markets (e.g. the Trinomial Model).............................. 3.25 Incomplete Markets (e.g. Non-tradable Underlying Asset).............. References................................................................................................... 337 342 349 353
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| adam_txt |
Contents 1 Volatilities. 1.1 Volatility I: Historical Volatility. 1.2 Volatility II: ARCH Models. 1.3 Volatility III: How to Use and Forecast Volatility. 1.4 Volatility IV: Magnitude of the Historical Volatility oftheS P500. 1.5 Volatility V: Volatility in Derivatives Pricing. 1.6 Derivatives Pricing with Time- (and Price-) Dependent Volatility: the Dupire Model. 1.7 Implied Volatility. .·. 1.8 Implied Volatilities of Call Options and Put Options with Same Expiration and Strike. 1.9 Volatility Skews, Volatility Smiles, and Volatility Surfaces. 1.10 Inferences From Implied Volatilities About the Market-Anticipated Distribution of the Underlying Asset’s Price. 1.11 Volatility Indices. 1.12 Basic Properties of the VIX. 1.13 Relation and CorrelationsBetween VIX and
SPX. 1.14 Influence of Price- and/or Time-Dependent Volatility on Delta, Gamma, and Theta. 1.15 Combined Trading of SPX and VIX for Hedging Purposes. 1.16 Relation and Correlations of VIX with Historical and Realized Volatility. 1.17 The СВОЕ S P500 Put Write Index. 1.18 The VIX Calculation Methodology. 1.19 The Volatility Weekend Effect. 1.20 Derivatives on the VIX: VIX Futures. 1.21 VIX Options. 1.22 Payoff and Profit Functions of a Trading Strategy for Combinations of SPX and VIX Options. References. 1 1 9 14 21 22 25 30 37 38 42 50 54 58 66 70 78 84 86 93 96 106 109 117 ix
Contents x 2 Extensions of the Black-Scholes Theory to Other Types of Options (Futures Options, Currency Options, American Options, Path-Dependent Options, Multi-asset Options). 119 Introduction and Discussions So Far . 119 Currency Options. 121 Futures Options. 126 Valuation of American Options and of Bermudan Options Through Backwardation (the Algorithm). 131 2.5 Valuation Examples for American Options in the Binomial and in the Wiener Model. 138 2.6 Hedging American Options. 142 2.7 Path-Dependent (Exotic) Derivatives, Definition and Examples . 144 2.8 Valuation of Path-Dependent Options, the Black-Scholes Formula for Path-Dependent Options. 150 2.9 Numerical Valuation Example of a Path-Dependent Option in a Three-Step Binomial Model (European and American). 155 2.10 The Complexity of Pricing Path-Dependent Options in an N-Step Binomial Model in General and, For Example, for Lookback Options. 157 2.11 Valuation of an American Lookback Option in a Four-Step Binomial Model (Numerical Example). 163 2.12 Explicit Formulas for European
Path-Dependent Options, For Example, В airier Options. 167 2.13 Explicit Formulas for European Path-Dependent Options, For Example, Geometric Asian Options. 170 2.14 Brief Comment on Hedging Path-Dependent Derivatives. 178 2.15 Valuation of Derivatives Using Monte Carlo Methods, Basic Principle. 179 2.16 Valuation of European Path-Dependent Derivatives with Monte Carlo Methods. 183 2.17 Monte Carlo Valuation of Asian Options. 184 2.18 Monte Carlo Valuation of Barrier Options. 185 2.19 Barrier Options in Turbo and Bonus Certificates . 189 2.20 Estimating Greeks (Especially Delta and Gamma) of Derivatives with Monte Carlo. 192 2.21 Estimating Delta and Delta Hedging for Path-Dependent Derivatives (e.g. Geometric Asian Option). 200 2.22 Some Fundamental Remarks on Monte Carlo Methods and on the Convergence of Monte Carlo Methods. 207 2.23 Some Remarks on Random Numbers. 212 2.24 A Remark on Quasi-Monte Carlo Methods. 217 2.25 An Example of Low-Discrepancy QMC Point Sets: The Hammersley Point
Sets. 226 2.26 Variance Reduction Methods for Monte Carlo. 229 2.1 2.2 2.3 2.4
Contents xi Using Monte Carlo with Control Variates to Value an Arithmetic Asian Option. 233 2.28 Multi-asset Options. 236 2.29 Modelling Correlated Financial Products in the Wiener Model, Cholesky Decomposition. 238 2.30 Valuation of Multi-asset Options. 242 2.31 Example of Pricing a Multi-asset Option with MC and with QMC. 245 References. 250 2.27 3 Fundamentals: Stochastic Analysis and Applications, Interest Rate Dynamics, and Basic Principles of Pricing Interest Rate Derivatives. 251 3.1 Modelling of Interest RateDynamics. 252 3.2 Differential Representation of Stochastic Processes: Heuristic Introduction. 254 3.3 Simulation of Ito Processes andBasic Models. 266 3.4 Excursus: The Ito Formula and Differential Notation oftheGBM. 275 3.5 Interest Rate Modelling Using Mean-Reverting Ornstein-
Uhlenbeck. 279 3.6 Examples of Interest Rate Derivatives and a Principal Methodology for Pricing such Derivatives. 285 3.7 Basic Concepts of Frictionless Interest Rate Markets: Zero-Coupon Bonds and Interest Rates. 287 3.8 Fixed and Floating Rate Coupon Bonds. 292 3.9 Interest Rate Swaps. 295 3.10 Valuation of Bond Prices and Interest Rate Derivatives in a Short-Rate Approach. 296 3.11 The Mean-Reverting Vasicek Model and the Hull-White Model for the Short Rate. 303 3.12 Affine Model Structures of Bond Prices. 304 3.13 Bond Prices in the Vasicek Model and Calibration in the Vasicek Model. 306 3.14 Bond Prices in the Hull-White Model and Calibration in the Hull-White Model. 308 3.15 Valuation and Put-Call Parity of Call and Put Options on Bond Prices. 311 3.16 Valuation of Caplets and Floorlets (as Well as Interest Rate Caps and Interest Rate Floors). 312 3.17 The Black-Scholes Differential
Equation. 316 3.18 The Stochastic Ito Integral: Heuristic Explanation and Basic Properties. 319 3.19 Conditional Expectations and Martingales. 330 3.20 The Feynman-Kac Formula. 333
xii Contents 3.21 The Black-Scholes Formula. 3.22 The Black-Scholes Model as a Complete Market and Hedging of Derivatives. 338 3.23 The Multidimensional Black-Scholes Model and Its Completeness. 341 3.24 Incomplete Markets (e.g. the Trinomial Model). 3.25 Incomplete Markets (e.g. Non-tradable Underlying Asset). References. 337 342 349 353 |
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| spelling | Larcher, Gerhard 1960- Verfasser (DE-588)1028526660 aut The art of quantitative finance Vol. 2 Volatilities, stochastic analysis and valuation tools Gerhard Larcher Cham Springer [2023] xii, 353 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier (DE-604)BV048910994 2 Erscheint auch als Online-Ausgabe 978-3-031-23870-3 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=034175212&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Larcher, Gerhard 1960- The art of quantitative finance |
| title | The art of quantitative finance |
| title_auth | The art of quantitative finance |
| title_exact_search | The art of quantitative finance |
| title_exact_search_txtP | The art of quantitative finance |
| title_full | The art of quantitative finance Vol. 2 Volatilities, stochastic analysis and valuation tools Gerhard Larcher |
| title_fullStr | The art of quantitative finance Vol. 2 Volatilities, stochastic analysis and valuation tools Gerhard Larcher |
| title_full_unstemmed | The art of quantitative finance Vol. 2 Volatilities, stochastic analysis and valuation tools Gerhard Larcher |
| title_short | The art of quantitative finance |
| title_sort | the art of quantitative finance volatilities stochastic analysis and valuation tools |
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