ADI Schemes for Pricing American Options under the Heston Model

DOI10.1080/1350486X.2015.1009129zbMath1396.91799arXiv1309.0110OpenAlexW3104970428MaRDI QIDQ4682480

Tinne Haentjens, Karel J. in 't Hout

Publication date: 18 September 2018

Published in: Applied Mathematical Finance (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.0110

zbMATH Keywords

American option pricinglinear complementarity problemalternating direction implicit schemesHeston modelIkonen-Toivanen splitting

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items (22)

High-performance computation of pricing two-asset American options under the Merton jump-diffusion model on a GPU ⋮ The Parareal Algorithm and the Sparse Grid Combination Technique in the Application of the Heston Model ⋮ Bilateral XVA pricing under stochastic default intensity: PDE modelling and computation ⋮ Uncertainty Quantification of Derivative Instruments ⋮ Efficient exposure computation by risk factor decomposition ⋮ Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing ⋮ Numerical Study of Splitting Methods for American Option Valuation ⋮ A New Approach for American Option Pricing: The Dynamic Chebyshev Method ⋮ A new stability result for the modified Craig-Sneyd scheme applied to two-dimensional convection-diffusion equations with mixed derivatives ⋮ Operator splitting schemes for American options under the two-asset Merton jump-diffusion model ⋮ An ADI Sparse Grid method for Pricing Efficiently American Options under the Heston Model ⋮ A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options ⋮ Deep learning for CVA computations of large portfolios of financial derivatives ⋮ Pricing European and American options under Heston model using discontinuous Galerkin finite elements ⋮ Analytic solutions for variance swaps with double-mean-reverting volatility ⋮ AMF-type W-methods for Parabolic Problems with Mixed Derivatives ⋮ American-type basket option pricing: a simple two-dimensional partial differential equation ⋮ Modulus-based successive overrelaxation iteration method for pricing American options with the two-asset Black-Scholes and Heston's models based on finite volume discretization ⋮ A semi-Lagrangian mixed finite element method for advection-diffusion variational inequalities ⋮ PRICING AMERICAN OPTIONS WITH THE RUNGE–KUTTA–LEGENDRE FINITE DIFFERENCE SCHEME ⋮ A finite volume–alternating direction implicit method for the valuation of American options under the Heston model ⋮ A case study on pricing foreign exchange options using the modified Craig–Sneyd ADI scheme

Cites Work

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• Stability of central finite difference schemes for the Heston PDE
• Stability of the modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term
• Operator splitting methods for pricing American options under stochastic volatility
• Stability of ADI schemes applied to convection--diffusion equations with mixed derivative terms
• Pricing American options using a space-time adaptive finite difference method
• Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms
• An alternating-direction implicit scheme for parabolic equations with mixed derivatives
• On multigrid for linear complementarity problems with application to American-style options
• Operator splitting methods for American option pricing.
• An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms
• Efficient and stable numerical solution of the Heston–Cox–Ingersoll–Ross partial differential equation by alternating direction implicit finite difference schemes
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems
• A tree-based method to price American options in the Heston model
• Multigrid for American option pricing with stochastic volatility
• A Projected Algebraic Multigrid Method for Linear Complementarity Problems
• COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• A Fourier-Based Valuation Method for Bermudan and Barrier Options under Heston's Model
• Efficient numerical methods for pricing American options under stochastic volatility
• Alternating direction methods for parabolic equations in two space dimensions with a mixed derivative
• Parabolic ADI Methods for Pricing American Options on Two Stocks
• ADI finite difference schemes for option pricing in the Heston model with correlation

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