Introduction to Stochastic Finance with Market Examples:
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| Previous Title: | Privault, Nicolas Stochastic Finance |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
CRC Press
2023
|
| Edition: | second edition |
| Series: | Chapman & Hall/CRC Financial Mathematics Series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 652 Seiten |
| ISBN: | 9781032288260 9781032288277 |
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| adam_text | Contents Preface Introduction ix 1 1 Assets, Portfolios, and Arbitrage 1.1 Portfolio Allocation and Short Selling ............................................................. 1.2 Arbitrage............................................................................................................... 1.3 Risk-Neutral Probability Measures................................................................... 1.4 Hedging of Contingent Claims ................................................................... 1.5 Market Completeness ......................................................................................... 1.6 Example: Binary Market ................................................................................... Exercises ........................................................................................................................ 15 15 17 21 25 27 27 34 2 Discrete-Time Market Model 2.1 Discrete-Time Compounding ............................................................................ 2.2 Arbitrage and Self-Financing Portfolios .......................................................... 2.3 Contingent Claims............................................................................................... 2.4 Martingales and Conditional Expectations .................................................... 2.5 Market Completeness and Risk-Neutral Measures ....................................... 2.6 The Cox-Ross-Rubinstein (CRR) Market Model.......................................... Exercises
........................................................................................................................ 39 39 41 47 50 54 56 60 3 Pricing and Hedging in Discrete Time 3.1 Pricing Contingent Claims ............................................................................... 3.2 Pricing Vanilla Options in the CRR Model .................................................... 3.3 Hedging Contingent Claims............................................................................... 3.4 Hedging Vanilla Options ........................ 3.5 Hedging Exotic Options..................................................................................... 3.6 Convergence of the CRR Model ...................................................................... Exercises ......................................................................................................................... 65 65 69 74 75 83 89 94 4 Brownian Motion and StochasticCalculus 113 4.1 Brownian Motion .............................................................................................. 113 4.2 Three Constructions of Brownian Motion ...................................................... 115 4.3 Wiener Stochastic Integral ............................................................................... 118 4.4 Itô Stochastic Integral........................................................................................ 126 4.5 Stochastic Calculus ........................................................................................... 132 Exercises
........................................................................................................................ 142 v
vi Contents 5 Continuous-Time Market Model 153 5.1 Asset Price Modeling .......................................................................................... 153 5.2 Arbitrage and Risk-Neutral Measures .............................................................. 154 5.3 Self-Financing Portfolio Strategies .................................................................... 156 5.4 Two-Asset Portfolio Model ................................................................................. 1$$ 5.5 Geometric Brownian Motion .............................................................................. 434 Exercises ......................................................................................................................... 167 6 Black-Scholes Pricing and Hedging 173 6.1 The Black-Scholes PDE...................................................................................... 173 6.2 European Call Options ...................................................................................... 177 6.3 European Put Options ...................................................................................... 183 6.4 Market Terms and Data...................................................................................... 187 6.5 The Heat Equation ............................................................................................ Ιθθ 6.6 Solution of the Black-Scholes PDE .................................................................. 1θ4 Exercises
......................................................................................................................... 197 7 Martingale Approach to Pricing and Hedging 207 7.1 Martingale Property of the Itô Integral ............................................................ 207 7.2 Risk-Neutral Probability Measures..................................................................... 211 7.3 Change of Measure and the Girsanov Theorem............................................... 215 7.4 Pricing by the Martingale Method..................................................................... 217 7.5 Hedging by the Martingale Method .................................................................. 223 Exercises ......................................................................................................................... 228 8 Stochastic Volatility 8.1 Stochastic Volatility Models ............................................................................. 8.2 Realized Variance Swaps ................................................................................... 8.3 Realized Variance Options ................................................................................ 8.4 European Options - PDE Method................................................................... 8.5 Perturbation Analysis........................................................................................ Exercises ........................................................................................................................ 9 Volatility Estimation 277 9.1 Historical
Volatility ............................................................................................ 277 9.2 Implied Volatility ............................................................................................... 279 9.3 Local Volatility .................................................................................................. 2g$ 9.4 The VIX® Index................................................................................................... ’ շցօ Exercises ............................................................................................................... շց$ 249 249 252 256 263 269 273 10 Maximum of Brownian Motion շցց 10.1 Running Maximum of Brownian Motion................................... 10.2 The Reflection Principle............................................... $θθ 10.3 Density of the Maximum of Brownian Motion ....................... 3Q4 10.4 Average of Geometric Brownian Extrema...................... „ Exercises ........................... .......................................... ........................................................................................ 320
Contents 11 Barrier Options 11.1 Options on Extrema............................................................................................. 11.2 Knock-Out Barrier................................................................................................ 11.3 Knock-In Barrier................................................................................................... 11.4 PDE Method......................................................................................................... 11.5 Hedging Barrier Options ................................................................................... Exercises ......................................................................................................................... 12 Lookback Options 12.1 The Lookback Put Option ................................................................................ 12.2 PDE Method.......................................................................................................... 12.3 The Lookback Call Option ................................................................................ 12.4 Delta Hedging for Lookback Options .............................................................. Exercises ......................................................................................................................... 13 Asian Options 13.1 Bounds on Asian Option Prices ....................................................................... 13.2 Hartman-Watson Distribution .......................................................................... 13.3 Laplace
Transform Method................................................................................ 13.4 Moment Matching Approximations ................................................................. 13.5 PDE Method..................................... Exercises ......................................................................................................................... 14 Optimal Stopping Theorem 14.1 Filtrations and Information Flow....................................................................... 14.2 Submartingales and Supermartingales.............................................................. 14.3 Optimal Stopping Theorem................................................................................ 14.4 Drifted Brownian Motion .................................................................................... Exercises ......................................................................................................................... 15 American Options 15.1 Perpetual American Put Options....................................................................... 15.2 PDE Method for Perpetual Put Options ........................................................ 15.3 Perpetual American Call Options ..................................... 15.4 Finite Expiration American Options................................................................. 15.5 PDE Method with Finite Expiration................................................................. Exercises
......................................................................................................................... 16 Change of Numéraire and Forward Measures 16.1 Notion of Numéraire............................................................................................. 16.2 Change of Numéraire .......................................................................................... 16.3 Foreign Exchange ................................................................................................. 16.4 Pricing Exchange Options ................................................................................. 16.5 Hedging by Change of Numéraire .......................................................... Exercises ......................................................................................................................... 17 Short Rates and Bond Pricing 17.1 Vasicek Model ....................................................................................................... 17.2 Affine Short Rate Models.................................................................................... 17.3 Zero-Coupon and Coupon Bonds....................................................................... 17.4 Bond Pricing PDE................................................................................................. Exercises ......................................................................................................................... vii 323 323 327 337 340 344 345 349 349 351 356 363 368 371 371 377 380 380 386 395 401 401 401 404 410 415 419 419
424 428 431 434 438 449 449 451 460 467 469 ^% 479 479 485 488 491 5θ$
Contents viii 18 Forward Rates 18.1 Construction of Forward Rates........................................................................... 18.2 LIBOR/SOFR Swap Rates ................................................................................. 18.3 The HJM Model.................................................................................................... 18.4 Yield Curve Modeling........................................................................................... 18.5 Two-Factor Model................................................................................................. 18.6 The BGM Model.................................................................................................... Exercises ......................................................................................................................... 19 Pricing of Interest Rate Derivatives 19.1 Forward Measures andTenor Structure ........................................................... 19.2 Bond Options ....................................................................................................... 19.3 Caplet Pricing ....................................................................................................... 19.4 Forward Swap Measures........................................................................................ 19.5 Swaption Pricing.................................................................................................... Exercises
......................................................................................................................... 20 Stochastic Calculus for Jump Processes 20.1 The Poisson Process.............................................................................................. 20.2 Compound Poisson Process................................................................................. 20.3 Stochastic Integrals and Itô Formula with Jumps............................................ 20.4 Stochastic DifferentialEquations with Jumps.................................................... 20.5 Girsanov Theorem for Jump Processes ............................................................ Exercises ......................................................................................................................... 21 Pricing and Hedging in Jump Models 543 543 343 343 333 333 333 565 333 571 576 585 589 595 601 21.1 Fitting the Distribution of Market Returns ..................................................... 601 21.2 Risk-Neutral Probability Measures..................................................................... 608 21.3 Pricing in Jump Models....................................................................................... 609 21.4 Exponential Lévy Models.................................................................................... 611 21.5 Black-Scholes PDE with Jumps ....................................................................... 614 21.6 Mean-Variance Hedging with Jumps................................................................. 616
Exercises ........................................................................................................................ 619 22 Basic Numerical Methods 22.1 Discretized Heat Equation ................................................................................. 22.2 Discretized Black-ScholesPDE............................................................................ 22.3 Euler Discretization .............................................................................................. 22.4 Milshtein Discretization........................................................................................ Exercises ...................................................................................................................... Bibliography Index 623 623 626 628 629 630 R41
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| adam_txt |
Contents Preface Introduction ix 1 1 Assets, Portfolios, and Arbitrage 1.1 Portfolio Allocation and Short Selling . 1.2 Arbitrage. 1.3 Risk-Neutral Probability Measures. 1.4 Hedging of Contingent Claims . 1.5 Market Completeness . 1.6 Example: Binary Market . Exercises . 15 15 17 21 25 27 27 34 2 Discrete-Time Market Model 2.1 Discrete-Time Compounding . 2.2 Arbitrage and Self-Financing Portfolios . 2.3 Contingent Claims. 2.4 Martingales and Conditional Expectations . 2.5 Market Completeness and Risk-Neutral Measures . 2.6 The Cox-Ross-Rubinstein (CRR) Market Model. Exercises
. 39 39 41 47 50 54 56 60 3 Pricing and Hedging in Discrete Time 3.1 Pricing Contingent Claims . 3.2 Pricing Vanilla Options in the CRR Model . 3.3 Hedging Contingent Claims. 3.4 Hedging Vanilla Options . 3.5 Hedging Exotic Options. 3.6 Convergence of the CRR Model . Exercises . 65 65 69 74 75 83 89 94 4 Brownian Motion and StochasticCalculus 113 4.1 Brownian Motion . 113 4.2 Three Constructions of Brownian Motion . 115 4.3 Wiener Stochastic Integral . 118 4.4 Itô Stochastic Integral. 126 4.5 Stochastic Calculus . 132 Exercises
. 142 v
vi Contents 5 Continuous-Time Market Model 153 5.1 Asset Price Modeling . 153 5.2 Arbitrage and Risk-Neutral Measures . 154 5.3 Self-Financing Portfolio Strategies . 156 5.4 Two-Asset Portfolio Model . 1$$ 5.5 Geometric Brownian Motion . 434 Exercises . 167 6 Black-Scholes Pricing and Hedging 173 6.1 The Black-Scholes PDE. 173 6.2 European Call Options . 177 6.3 European Put Options . 183 6.4 Market Terms and Data. 187 6.5 The Heat Equation . Ιθθ 6.6 Solution of the Black-Scholes PDE . 1θ4 Exercises
. 197 7 Martingale Approach to Pricing and Hedging 207 7.1 Martingale Property of the Itô Integral . 207 7.2 Risk-Neutral Probability Measures. 211 7.3 Change of Measure and the Girsanov Theorem. 215 7.4 Pricing by the Martingale Method. 217 7.5 Hedging by the Martingale Method . 223 Exercises . 228 8 Stochastic Volatility 8.1 Stochastic Volatility Models . 8.2 Realized Variance Swaps . 8.3 Realized Variance Options . 8.4 European Options - PDE Method. 8.5 Perturbation Analysis. Exercises . 9 Volatility Estimation 277 9.1 Historical
Volatility . 277 9.2 Implied Volatility . 279 9.3 Local Volatility . 2g$ 9.4 The VIX® Index. ’ շցօ Exercises . շց$ 249 249 252 256 263 269 273 10 Maximum of Brownian Motion շցց 10.1 Running Maximum of Brownian Motion. 10.2 The Reflection Principle. ' $θθ 10.3 Density of the Maximum of Brownian Motion . 3Q4 10.4 Average of Geometric Brownian Extrema. „ Exercises . . . 320
Contents 11 Barrier Options 11.1 Options on Extrema. 11.2 Knock-Out Barrier. 11.3 Knock-In Barrier. 11.4 PDE Method. 11.5 Hedging Barrier Options . Exercises . 12 Lookback Options 12.1 The Lookback Put Option . 12.2 PDE Method. 12.3 The Lookback Call Option . 12.4 Delta Hedging for Lookback Options . Exercises . 13 Asian Options 13.1 Bounds on Asian Option Prices . 13.2 Hartman-Watson Distribution . 13.3 Laplace
Transform Method. 13.4 Moment Matching Approximations . 13.5 PDE Method. Exercises . 14 Optimal Stopping Theorem 14.1 Filtrations and Information Flow. 14.2 Submartingales and Supermartingales. 14.3 Optimal Stopping Theorem. 14.4 Drifted Brownian Motion . Exercises . 15 American Options 15.1 Perpetual American Put Options. 15.2 PDE Method for Perpetual Put Options . 15.3 Perpetual American Call Options . 15.4 Finite Expiration American Options. 15.5 PDE Method with Finite Expiration. Exercises
. 16 Change of Numéraire and Forward Measures 16.1 Notion of Numéraire. 16.2 Change of Numéraire . 16.3 Foreign Exchange . 16.4 Pricing Exchange Options . 16.5 Hedging by Change of Numéraire . Exercises . 17 Short Rates and Bond Pricing 17.1 Vasicek Model . 17.2 Affine Short Rate Models. 17.3 Zero-Coupon and Coupon Bonds. 17.4 Bond Pricing PDE. Exercises . vii 323 323 327 337 340 344 345 349 349 351 356 363 368 371 371 377 380 380 386 395 401 401 401 404 410 415 419 419
424 428 431 434 438 449 449 451 460 467 469 ^% 479 479 485 488 491 5θ$
Contents viii 18 Forward Rates 18.1 Construction of Forward Rates. 18.2 LIBOR/SOFR Swap Rates . 18.3 The HJM Model. 18.4 Yield Curve Modeling. 18.5 Two-Factor Model. 18.6 The BGM Model. Exercises . 19 Pricing of Interest Rate Derivatives 19.1 Forward Measures andTenor Structure . 19.2 Bond Options . 19.3 Caplet Pricing . 19.4 Forward Swap Measures. 19.5 Swaption Pricing. Exercises
. 20 Stochastic Calculus for Jump Processes 20.1 The Poisson Process. 20.2 Compound Poisson Process. 20.3 Stochastic Integrals and Itô Formula with Jumps. 20.4 Stochastic DifferentialEquations with Jumps. 20.5 Girsanov Theorem for Jump Processes . Exercises . 21 Pricing and Hedging in Jump Models 543 543 343 343 333 333 333 565 333 571 576 585 589 595 601 21.1 Fitting the Distribution of Market Returns . 601 21.2 Risk-Neutral Probability Measures. 608 21.3 Pricing in Jump Models. 609 21.4 Exponential Lévy Models. 611 21.5 Black-Scholes PDE with Jumps . 614 21.6 Mean-Variance Hedging with Jumps. 616
Exercises . 619 22 Basic Numerical Methods 22.1 Discretized Heat Equation . 22.2 Discretized Black-ScholesPDE. 22.3 Euler Discretization . 22.4 Milshtein Discretization. Exercises . Bibliography Index 623 623 626 628 629 630 R41 |
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| index_date | 2024-07-03T21:18:59Z |
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| spelling | Privault, Nicolas Verfasser (DE-588)1032387327 aut Introduction to Stochastic Finance with Market Examples second edition Boca Raton CRC Press 2023 X, 652 Seiten txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC Financial Mathematics Series Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Stochastik (DE-588)4121729-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-003-29867-0 Vorangegangen ist Privault, Nicolas Stochastic Finance 2014 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034023333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Privault, Nicolas Introduction to Stochastic Finance with Market Examples Finanzmathematik (DE-588)4017195-4 gnd Stochastik (DE-588)4121729-9 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4121729-9 |
| title | Introduction to Stochastic Finance with Market Examples |
| title_auth | Introduction to Stochastic Finance with Market Examples |
| title_exact_search | Introduction to Stochastic Finance with Market Examples |
| title_exact_search_txtP | Introduction to Stochastic Finance with Market Examples |
| title_full | Introduction to Stochastic Finance with Market Examples |
| title_fullStr | Introduction to Stochastic Finance with Market Examples |
| title_full_unstemmed | Introduction to Stochastic Finance with Market Examples |
| title_old | Privault, Nicolas Stochastic Finance |
| title_short | Introduction to Stochastic Finance with Market Examples |
| title_sort | introduction to stochastic finance with market examples |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Stochastik (DE-588)4121729-9 gnd |
| topic_facet | Finanzmathematik Stochastik |
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