Variational Analysis for the Black and Scholes Equation with Stochastic Volatility

DOI10.1051/m2an:2002018zbMath1137.91421OpenAlexW2061956999MaRDI QIDQ4423060

Yves Achdou, Nicoletta Tchou

Publication date: 25 August 2003

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2002__36_3_373_0

zbMATH Keywords

finite element methodfinite difference methodweighted Sobolev spacesdegenerate parabolic equationseuropean optionsmean reverting Ornstein-Uhlenbeck process

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Degenerate parabolic equations (35K65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Derivative securities (option pricing, hedging, etc.) (91G20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (13)

Variational Analysis for Options with Stochastic Volatility and Multiple Factors ⋮ The evaluation of American options in a stochastic volatility model with jumps: an efficient finite element approach ⋮ Analytic approach to solve a degenerate parabolic PDE for the Heston model ⋮ Two‐dimensional Haar wavelet based approximation technique to study the sensitivities of the price of an option ⋮ A wavelet‐based novel approximation to investigate the sensitivities of various path‐independent binary options ⋮ A finite element discretization method for option pricing with the Bates model ⋮ Real options pricing by the finite element method ⋮ A computational method to price with transaction costs under the nonlinear Black-Scholes model ⋮ Accuracy, robustness, and efficiency of the linear boundary condition for the Black-Scholes equations ⋮ Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces ⋮ Reconstructing local volatility using total variation ⋮ A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization ⋮ DG framework for pricing European options under one-factor stochastic volatility models

Uses Software

• FreeFem++

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• A finite element approximation for a class of degenerate elliptic equations
• Stock Price Distributions with Stochastic Volatility: An Analytic Approach
• The Identity of Weak and Strong Extensions of Differential Operators
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