Coverart for item
The Resource PDE and martingale methods in option pricing, Andrea Pascucci

PDE and martingale methods in option pricing, Andrea Pascucci

Label
PDE and martingale methods in option pricing
Title
PDE and martingale methods in option pricing
Statement of responsibility
Andrea Pascucci
Creator
Subject
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
Member of
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
Instantiates
Publication
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 Put-Call parity formula""; ""1.2 Risk-neutral price and arbitrage pricing""; ""1.2.1 Risk-neutral price""; ""1.2.2 Risk-neutral probability""; ""1.2.3 Arbitrage price""; ""1.2.4 A generalization of the Put-Call parity""; ""1.2.5 Incomplete markets""
  • ""2 Discrete market models""""2.1 Discrete markets and arbitrage strategies""; ""2.1.1 Self-financing 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 arbitrage-free 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 Black-Scholes formula""; ""2.3.6 Black-Scholes 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 Free-boundary problem for American options""; ""2.5.6 American and European options in the binomial model""; ""3 Continuous-time 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 Riemann-Stieltjes integral""; ""3.4.1 Bounded-variation functions""
  • ""3.4.2 Riemann-Stieltjes 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 L2-processes""; ""4.3.1 Ito and Riemann-Stieltjes 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 Co-variation process""; ""4.4 Integral of L2loc-processes""; ""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
10.1007/978-88-470-1781-8
http://library.link/vocab/ext/overdrive/overdriveId
978-88-470-1780-1
Specific material designation
remote
System control number
(OCoLC)728100148
Label
PDE and martingale methods in option pricing, Andrea Pascucci
Publication
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 Put-Call parity formula""; ""1.2 Risk-neutral price and arbitrage pricing""; ""1.2.1 Risk-neutral price""; ""1.2.2 Risk-neutral probability""; ""1.2.3 Arbitrage price""; ""1.2.4 A generalization of the Put-Call parity""; ""1.2.5 Incomplete markets""
  • ""2 Discrete market models""""2.1 Discrete markets and arbitrage strategies""; ""2.1.1 Self-financing 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 arbitrage-free 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 Black-Scholes formula""; ""2.3.6 Black-Scholes 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 Free-boundary problem for American options""; ""2.5.6 American and European options in the binomial model""; ""3 Continuous-time 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 Riemann-Stieltjes integral""; ""3.4.1 Bounded-variation functions""
  • ""3.4.2 Riemann-Stieltjes 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 L2-processes""; ""4.3.1 Ito and Riemann-Stieltjes 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 Co-variation process""; ""4.4 Integral of L2loc-processes""; ""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
10.1007/978-88-470-1781-8
http://library.link/vocab/ext/overdrive/overdriveId
978-88-470-1780-1
Specific material designation
remote
System control number
(OCoLC)728100148

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