Nonlinear Option Pricing

by Guyon, Julien

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Title Statements

Full title :Nonlinear Option Pricing.

Summary

Option Pricing in a Nutshell The super-replication paradigmStochastic representation of solutions of linear PDEsMonte Carlo The Monte Carlo method Euler discretization error Romberg extrapolationSome Excursions in Option Pricing Complete market modelsBeyond replication and super-replicationNonlinear PDEs: A Bit of Theory Nonlinear second order parabolic PDEs: some generalitiesWhy is a pricing equation a parabolic PDE? Finite difference schemesStochastic control and the Hamilton-Jacobi-Bellman PDEViscosity solutionsExamples of Nonlinear Problems in Finance American options The uncertain volatility modelTransaction costs: Leland's model Illiquid markets Super-replication under delta and gamma constraintsThe uncertain mortality model for reinsurance deals Credit valuation adjustment The passport optionEarly Exercise Problems Super-replication of American options American options and semilinear PDEs The dual method for American options On the ownership of the exercise right On the finiteness of exercise dates On the accounting of multiple coupons Finite difference methods for American options Monte Carlo methods for American optionsCase study: pricing and hedging of a multi-asset convertible bondIntroduction to chooser options Regression methods for chooser options The dual algorithm for chooser options Numerical examples of pricing of chooser optionsBackward Stochastic Differential Equations First order BSDEsReflected first order BSDEsSecond order BSDEsThe Uncertain Lapse and Mortality Model Reinsurance deals The deterministic lapse and mortality model The uncertain lapse and mortality model Path-dependent payoffs Pricing the option on the up-and-out barrier An example of PDE implementation Monte Carlo pricing Monte Carlo pricing of the option on the up-and-out barrier Link with first order BSDEs Numerical results using PDENumerical results using.

Monte CarloThe Uncertain Volatility Model Introduction The model The parametric approachSolving the UVM with BSDEs Numerical experimentsMcKean Nonlinear Stochastic Differential Equations Definition The particle method in a nutshell Propagation of chaos and convergence of the particle methodCalibration of Local Stochastic Volatility Models to Market Smiles Introduction The calibration condition Existence of the calibrated local stochastic volatility model The PDE method The Markovian projection method The particle methodAdding stochastic interest ratesThe particle method: numerical testsCalibration of Local Correlation Models to Market Smiles Introduction The FX triangle smile calibration problem A new representation of admissible correlations The particle method for local correlation Some examples of pairs of functions (a, b) Some links between local correlationsJoint extrapolation of local volatilities Price impact of correlationThe equity index smile calibration problem Numerical experiments on the FX triangle problemGeneralization to stochastic volatility, stochastic interest rates, and stochastic dividend yieldPath-dependent volatilityMarked Branching Diffusions Nonlinear Monte Carlo algorithms for some semilinear PDEs Branching diffusions Marked branching diffusions Application: Credit valuation adjustment algorithmSystem of semilinear PDEs Nonlinear PDEsReferences IndexExercises appear at the end of each chapter.

Edition Statements

Publication Date:©2013.

Publication Statements

Publisher(s):CRC Press
Place of Publication:Bosa Roca
Language:eng
Publication Date:©2013.

The Physical Object

Description:1 online resource (480 pages).

Edition Identifiers

ISBN:9781466570344, 1466570342
oclc:on1058352251
LC Classification:HG6042 ǂb .G89 2014eb
Dewey Decimal:332.64

Front Cover -- Dedication -- Contents -- Preface -- List of Figures -- List of Tables -- Chapter 1: Option Pricing in a Nutshell -- Chapter 2: Monte Carlo -- Chapter 3: Some Excursions in Option Pricing -- Chapter 4: Nonlinear PDEs: A Bit of Theory -- Chapter 5: Examples of Nonlinear Problems in Finance -- Chapter 6: Early Exercise Problems -- Chapter 7: Backward Stochastic Differential Equations -- Chapter 8: The Uncertain Lapse and Mortality Model -- Chapter 9: The Uncertain Volatility Model -- Chapter 10: McKean Nonlinear Stochastic Differential Equations -- Chapter 11: Calibration of Local Stochastic Volatility Models to Market Smiles -- Chapter 12: Calibration of Local Correlation Models to Market Smiles -- Chapter 13: Marked Branching Diffusions -- References.

Subjects

Business mathematics Mathématiques financières Nonlinear pricing -- Mathematical models Options (Finance) -- Prices Options (Finances) -- Prix Tarification non linéaire -- Modèles ma…