The Resource PDE and martingale methods in option pricing, Andrea Pascucci
PDE and martingale methods in option pricing, Andrea Pascucci
Resource Information
The item PDE and martingale methods in option pricing, Andrea Pascucci represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item PDE and martingale methods in option pricing, Andrea Pascucci represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform
 Language
 eng
 Extent
 1 online resource (xvii, 719 pages).
 Contents

 ""Title Page ""; ""Copyright Page ""; ""Preface""; ""Table of Contents ""; ""General notations""; ""Shortenings""; ""Function spaces""; ""Spaces of processes""; ""1 Derivatives and arbitrage pricing""; ""1.1 Options""; ""1.1.1 Main purposes""; ""1.1.2 Main problems""; ""1.1.3 Rules of compounding""; ""1.1.4 Arbitrage opportunities and PutCall parity formula""; ""1.2 Riskneutral price and arbitrage pricing""; ""1.2.1 Riskneutral price""; ""1.2.2 Riskneutral probability""; ""1.2.3 Arbitrage price""; ""1.2.4 A generalization of the PutCall parity""; ""1.2.5 Incomplete markets""
 ""2 Discrete market models""""2.1 Discrete markets and arbitrage strategies""; ""2.1.1 Selffinancing and predictable strategies""; ""2.1.2 Normalized market""; ""2.1.3 Arbitrage opportunities and admissible strategies""; ""2.1.4 Equivalent martingale measure""; ""2.1.5 Change of numeraire""; ""2.2 European derivatives""; ""2.2.1 Pricing in an arbitragefree market""; ""2.2.2 Completeness""; ""2.2.3 Fundamental theorems of asset pricing""; ""2.2.4 Markov property""; ""2.3 Binomial model""; ""2.3.1 Martingale measure and arbitrage price""; ""2.3.2 Hedging strategies""
 ""2.3.3 Binomial algorithm""""2.3.4 Calibration""; ""2.3.5 Binomial model and BlackScholes formula""; ""2.3.6 BlackScholes differential equation""; ""2.4 Trinomial model""; ""2.4.1 Pricing and hedging in an incomplete market""; ""2.5 American derivatives""; ""2.5.1 Arbitrage price""; ""2.5.2 Optimal exercise strategies""; ""2.5.3 Pricing and hedging algorithms""; ""2.5.4 Relations with European options""; ""2.5.5 Freeboundary problem for American options""; ""2.5.6 American and European options in the binomial model""; ""3 Continuoustime stochastic processes""
 ""3.1 Stochastic processes and real Brownian motion""""3.1.1 Markov property""; ""3.1.2 Brownian motion and the heat equation""; ""3.2 Uniqueness""; ""3.2.1 Law of a continuous process""; ""3.2.2 Equivalence of processes""; ""3.2.3 Modifications and indistinguishable processes""; ""3.2.4 Adapted and progressively measurable processes""; ""3.3 Martingales""; ""3.3.1 Doobâ€?s inequality""; ""3.3.2 Martingale spaces: M2 and M2""; ""3.3.3 The usual hypotheses""; ""3.3.4 Stopping times and martingales""; ""3.4 RiemannStieltjes integral""; ""3.4.1 Boundedvariation functions""
 ""3.4.2 RiemannStieltjes integral and Ito formula""""3.4.3 Regularity of the paths of a Brownian motion""; ""4 Brownian integration""; ""4.1 Stochastic integral of deterministic functions""; ""4.2 Stochastic integral of simple processes""; ""4.3 Integral of L2processes""; ""4.3.1 Ito and RiemannStieltjes integral""; ""4.3.2 Ito integral and stopping times""; ""4.3.3 Quadratic variation process""; ""4.3.4 Martingales with bounded variation""; ""4.3.5 Covariation process""; ""4.4 Integral of L2locprocesses""; ""4.4.1 Local martingales""; ""4.4.2 Localization and quadratic variation""
 Isbn
 9788847017818
 Label
 PDE and martingale methods in option pricing
 Title
 PDE and martingale methods in option pricing
 Statement of responsibility
 Andrea Pascucci
 Subject

 Differential equations, Partial
 Differential equations, Partial
 Martingales (Mathematics)
 Martingales (Mathematics)
 Martingales (Mathematics)
 Options (Finance)  Prices  Mathematical models
 Options (Finance)  Prices  Mathematical models
 Options (Finance)  Prices  Mathematical models
 Differential equations, Partial
 Language
 eng
 Summary
 This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Pascucci, Andrea
 Dewey number
 332.63/228
 Index
 index present
 LC call number
 HG6024.A3
 LC item number
 P37 2011
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Bocconi & Springer Series,
 http://library.link/vocab/subjectName

 Options (Finance)
 Martingales (Mathematics)
 Differential equations, Partial
 Differential equations, Partial
 Martingales (Mathematics)
 Options (Finance)
 Label
 PDE and martingale methods in option pricing, Andrea Pascucci
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 ""Title Page ""; ""Copyright Page ""; ""Preface""; ""Table of Contents ""; ""General notations""; ""Shortenings""; ""Function spaces""; ""Spaces of processes""; ""1 Derivatives and arbitrage pricing""; ""1.1 Options""; ""1.1.1 Main purposes""; ""1.1.2 Main problems""; ""1.1.3 Rules of compounding""; ""1.1.4 Arbitrage opportunities and PutCall parity formula""; ""1.2 Riskneutral price and arbitrage pricing""; ""1.2.1 Riskneutral price""; ""1.2.2 Riskneutral probability""; ""1.2.3 Arbitrage price""; ""1.2.4 A generalization of the PutCall parity""; ""1.2.5 Incomplete markets""
 ""2 Discrete market models""""2.1 Discrete markets and arbitrage strategies""; ""2.1.1 Selffinancing and predictable strategies""; ""2.1.2 Normalized market""; ""2.1.3 Arbitrage opportunities and admissible strategies""; ""2.1.4 Equivalent martingale measure""; ""2.1.5 Change of numeraire""; ""2.2 European derivatives""; ""2.2.1 Pricing in an arbitragefree market""; ""2.2.2 Completeness""; ""2.2.3 Fundamental theorems of asset pricing""; ""2.2.4 Markov property""; ""2.3 Binomial model""; ""2.3.1 Martingale measure and arbitrage price""; ""2.3.2 Hedging strategies""
 ""2.3.3 Binomial algorithm""""2.3.4 Calibration""; ""2.3.5 Binomial model and BlackScholes formula""; ""2.3.6 BlackScholes differential equation""; ""2.4 Trinomial model""; ""2.4.1 Pricing and hedging in an incomplete market""; ""2.5 American derivatives""; ""2.5.1 Arbitrage price""; ""2.5.2 Optimal exercise strategies""; ""2.5.3 Pricing and hedging algorithms""; ""2.5.4 Relations with European options""; ""2.5.5 Freeboundary problem for American options""; ""2.5.6 American and European options in the binomial model""; ""3 Continuoustime stochastic processes""
 ""3.1 Stochastic processes and real Brownian motion""""3.1.1 Markov property""; ""3.1.2 Brownian motion and the heat equation""; ""3.2 Uniqueness""; ""3.2.1 Law of a continuous process""; ""3.2.2 Equivalence of processes""; ""3.2.3 Modifications and indistinguishable processes""; ""3.2.4 Adapted and progressively measurable processes""; ""3.3 Martingales""; ""3.3.1 Doobâ€?s inequality""; ""3.3.2 Martingale spaces: M2 and M2""; ""3.3.3 The usual hypotheses""; ""3.3.4 Stopping times and martingales""; ""3.4 RiemannStieltjes integral""; ""3.4.1 Boundedvariation functions""
 ""3.4.2 RiemannStieltjes integral and Ito formula""""3.4.3 Regularity of the paths of a Brownian motion""; ""4 Brownian integration""; ""4.1 Stochastic integral of deterministic functions""; ""4.2 Stochastic integral of simple processes""; ""4.3 Integral of L2processes""; ""4.3.1 Ito and RiemannStieltjes integral""; ""4.3.2 Ito integral and stopping times""; ""4.3.3 Quadratic variation process""; ""4.3.4 Martingales with bounded variation""; ""4.3.5 Covariation process""; ""4.4 Integral of L2locprocesses""; ""4.4.1 Local martingales""; ""4.4.2 Localization and quadratic variation""
 Control code
 728100148
 Dimensions
 unknown
 Extent
 1 online resource (xvii, 719 pages).
 Form of item
 online
 Isbn
 9788847017818
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9788847017818
 http://library.link/vocab/ext/overdrive/overdriveId
 9788847017801
 Specific material designation
 remote
 System control number
 (OCoLC)728100148
 Label
 PDE and martingale methods in option pricing, Andrea Pascucci
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 ""Title Page ""; ""Copyright Page ""; ""Preface""; ""Table of Contents ""; ""General notations""; ""Shortenings""; ""Function spaces""; ""Spaces of processes""; ""1 Derivatives and arbitrage pricing""; ""1.1 Options""; ""1.1.1 Main purposes""; ""1.1.2 Main problems""; ""1.1.3 Rules of compounding""; ""1.1.4 Arbitrage opportunities and PutCall parity formula""; ""1.2 Riskneutral price and arbitrage pricing""; ""1.2.1 Riskneutral price""; ""1.2.2 Riskneutral probability""; ""1.2.3 Arbitrage price""; ""1.2.4 A generalization of the PutCall parity""; ""1.2.5 Incomplete markets""
 ""2 Discrete market models""""2.1 Discrete markets and arbitrage strategies""; ""2.1.1 Selffinancing and predictable strategies""; ""2.1.2 Normalized market""; ""2.1.3 Arbitrage opportunities and admissible strategies""; ""2.1.4 Equivalent martingale measure""; ""2.1.5 Change of numeraire""; ""2.2 European derivatives""; ""2.2.1 Pricing in an arbitragefree market""; ""2.2.2 Completeness""; ""2.2.3 Fundamental theorems of asset pricing""; ""2.2.4 Markov property""; ""2.3 Binomial model""; ""2.3.1 Martingale measure and arbitrage price""; ""2.3.2 Hedging strategies""
 ""2.3.3 Binomial algorithm""""2.3.4 Calibration""; ""2.3.5 Binomial model and BlackScholes formula""; ""2.3.6 BlackScholes differential equation""; ""2.4 Trinomial model""; ""2.4.1 Pricing and hedging in an incomplete market""; ""2.5 American derivatives""; ""2.5.1 Arbitrage price""; ""2.5.2 Optimal exercise strategies""; ""2.5.3 Pricing and hedging algorithms""; ""2.5.4 Relations with European options""; ""2.5.5 Freeboundary problem for American options""; ""2.5.6 American and European options in the binomial model""; ""3 Continuoustime stochastic processes""
 ""3.1 Stochastic processes and real Brownian motion""""3.1.1 Markov property""; ""3.1.2 Brownian motion and the heat equation""; ""3.2 Uniqueness""; ""3.2.1 Law of a continuous process""; ""3.2.2 Equivalence of processes""; ""3.2.3 Modifications and indistinguishable processes""; ""3.2.4 Adapted and progressively measurable processes""; ""3.3 Martingales""; ""3.3.1 Doobâ€?s inequality""; ""3.3.2 Martingale spaces: M2 and M2""; ""3.3.3 The usual hypotheses""; ""3.3.4 Stopping times and martingales""; ""3.4 RiemannStieltjes integral""; ""3.4.1 Boundedvariation functions""
 ""3.4.2 RiemannStieltjes integral and Ito formula""""3.4.3 Regularity of the paths of a Brownian motion""; ""4 Brownian integration""; ""4.1 Stochastic integral of deterministic functions""; ""4.2 Stochastic integral of simple processes""; ""4.3 Integral of L2processes""; ""4.3.1 Ito and RiemannStieltjes integral""; ""4.3.2 Ito integral and stopping times""; ""4.3.3 Quadratic variation process""; ""4.3.4 Martingales with bounded variation""; ""4.3.5 Covariation process""; ""4.4 Integral of L2locprocesses""; ""4.4.1 Local martingales""; ""4.4.2 Localization and quadratic variation""
 Control code
 728100148
 Dimensions
 unknown
 Extent
 1 online resource (xvii, 719 pages).
 Form of item
 online
 Isbn
 9788847017818
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9788847017818
 http://library.link/vocab/ext/overdrive/overdriveId
 9788847017801
 Specific material designation
 remote
 System control number
 (OCoLC)728100148
Subject
 Differential equations, Partial
 Differential equations, Partial
 Martingales (Mathematics)
 Martingales (Mathematics)
 Martingales (Mathematics)
 Options (Finance)  Prices  Mathematical models
 Options (Finance)  Prices  Mathematical models
 Options (Finance)  Prices  Mathematical models
 Differential equations, Partial
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