The evaluation of American options in a stochastic volatility model with jumps: an efficient finite element approach

DOI10.1016/j.camwa.2010.06.040zbMath1202.91313OpenAlexW1992192198MaRDI QIDQ614340

Carlo Sgarra, Luca Vincenzo Ballestra

Publication date: 27 December 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.06.040

zbMATH Keywords

finite elementsLévy processesstochastic volatilityoption pricing

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Numerical methods (including Monte Carlo methods) (91G60) 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)

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Cites Work

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• Unnamed Item
• A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions
• The Pricing of Options and Corporate Liabilities
• Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing
• A finite element discretization method for option pricing with the Bates model
• Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions
• Numerical solution of two asset jump diffusion models for option valuation
• Penalty methods for American options with stochastic volatility
• Operator splitting methods for American option pricing.
• A penalty method for American options with jump diffusion processes
• An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms
• Two singular diffusion problems
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• Quadratic Convergence for Valuing American Options Using a Penalty Method
• A Theory of the Term Structure of Interest Rates
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Wavelet Galerkin pricing of American options on Lévy driven assets
• Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes
• A FAST, STABLE AND ACCURATE NUMERICAL METHOD FOR THE BLACK–SCHOLES EQUATION OF AMERICAN OPTIONS
• Anatomy of high-performance matrix multiplication
• Lagrange Multiplier Approach with Optimized Finite Difference Stencils for Pricing American Options under Stochastic Volatility
• THE EVALUATION OF AMERICAN OPTION PRICES UNDER STOCHASTIC VOLATILITY AND JUMP-DIFFUSION DYNAMICS USING THE METHOD OF LINES
• Variational Analysis for the Black and Scholes Equation with Stochastic Volatility
• Multigrid for American option pricing with stochastic volatility
• Robust numerical methods for contingent claims under jump diffusion processes
• Stochastic Volatility for Lévy Processes
• Financial Modelling with Jump Processes
• A Componentwise Splitting Method for Pricing American Options Under the Bates Model
• COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY
• A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under Lévy Processes
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Efficient numerical methods for pricing American options under stochastic volatility
• Option pricing when underlying stock returns are discontinuous
• A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
• The representation of American options prices under stochastic volatility and jump-diffusion dynamics

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