Solution of option pricing equations using orthogonal polynomial expansion.

DOI10.21136/AM.2021.0361-19MaRDI QIDQ1984560

Jan Pospíšil, Kateřina Filipová, Falko Baustian

Publication date: 16 September 2021

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.06533

zbMATH Keywords

option pricingLaguerre polynomialHermite polynomialHeston modelorthogonal polynomial expansion

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) 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 (3)

Monotone methods in counterparty risk models with nonlinear Black-Scholes-type equations ⋮ The Heston stochastic volatility model has a boundary trace at zero volatility ⋮ Unnamed Item

Uses Software

• DLMF
• OPQ
• BENCHOP
• NDSolve

Cites Work

• The Pricing of Options and Corporate Liabilities
• Hermite polynomial based expansion of European option prices
• Discrete time Galerkin methods for a parabolic boundary value problem
• Piecewise Hermite interpolation in one and two variables with applications to partial differential equations
• On finite element approximations to time-dependent problems
• BENCHOP – The BENCHmarking project in option pricing
• The Heston Model and Its Extensions in Matlab and C#
• A Theory of the Term Structure of Interest Rates
• Market completion using options
• Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations
• Unifying pricing formula for several stochastic volatility models with jumps
• Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models
• Isogeometric analysis in option pricing
• Option pricing with orthogonal polynomial expansions
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Stock Price Distributions with Stochastic Volatility: An Analytic Approach
• Galerkin Finite Element Methods for Parabolic Problems
• Generalized Finite-Difference Schemes
• Galerkin Methods for Parabolic Equations
• A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Solution of option pricing equations using orthogonal polynomial expansion.