A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models

No abstract is available for this paper.

• Publication year

  2005

• Venue

  SIAM Journal on Numerical Analysis

• Publication date

  2005-04-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1137/S0036142903436186
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Equqtions D'Hamilton-Jacobi Du Premier Ordre Avec Termes Intégro-Différentiels

  2007cited by this paper
• A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations

  2006cited by this paper
• Integro-differential equations for option prices in exponential Lévy models

  2005influential reference
• Financial Modelling with Jump Processes

  2005cited by this paper
• A penalty method for American options with jump diffusion processes

  2004cited by this paper
• Non-parametric calibration of jump–diffusion option pricing models

  2004cited by this paper
• Financial Modelling with Jump Processes

  2003cited by this paper
• Lévy Processes in Finance: Pricing Financial Derivatives

  2003cited by this paper
• Calibration of Jump-Diffusion Option Pricing Models: A Robust Non-Parametric Approach

  2002cited by this paper
• Fast deterministic pricing of options on Lévy driven assets

  2002cited by this paper
• On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations

  2002cited by this paper
• Non-Gaussian Merton-Black-Scholes theory

  2002cited by this paper
• Second Order Elliptic Integro-Differential Problems

  2002cited by this paper
• Pure jump L'evy processes for asset price modeling

  2002cited by this paper
• Option Pricing, Interest Rates and Risk Management: Purely Discontinuous Asset Price Processes

  2001cited by this paper
• Application of Generalized Hyperbolic Lévy Motions to Finance

  2001cited by this paper
• Pseudo Differential Operators and Markov Processes: Volume I: Fourier Analysis and Semigroups

  2001cited by this paper
• On the rate of convergence of finite-difference approximations for Bellmans equations with variable coefficients

  2000cited by this paper
• Pricing Financial Instruments: The Finite Difference Method

  2000cited by this paper
• Pricing contingent claims on stocks driven by Lévy processes

  1999cited by this paper
• Option valuation using the fast Fourier transform

  1999cited by this paper
• Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing

  1999influential reference
• Optimal Stopping of Controlled Jump Diiusion Processes: a Viscosity Solution Approach

  1998cited by this paper
• Backward stochastic differential equations and integral-partial differential equations

  1997influential reference
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

  1997cited by this paper
• Processes of normal inverse Gaussian type

  1997cited by this paper
• Viscosity solutions of nonlinear integro-differential equations

  1996cited by this paper
• Pseudo-Differential Operators and Markov Processes

  1996cited by this paper
• Implicit-explicit methods for time-dependent partial differential equations

  1995influential reference
• Analyse numérique des options américaines dans un modèle de diffusion avec sauts

  1994cited by this paper
• User’s guide to viscosity solutions of second order partial differential equations

  1992cited by this paper
• Equqtions D'Hamilton-Jacobi Du Premier Ordre Avec Termes Intégro-Différentiels: Partie II: Unicité Des Solutions De Viscosité

  1991cited by this paper
• Option Pricing With V. G. Martingale Components

  1991cited by this paper
• Stochastic integration and differential equations

  1990cited by this paper
• Convergence of approximation schemes for fully nonlinear second order equations

  1990cited by this paper
• Optimal Control of Jump-Markov Processes and Viscosity Solutions

  1988cited by this paper
• Limit Theorems for Stochastic Processes

  1987cited by this paper
• Simulation of estimates using the empirical characteristic function

  1987cited by this paper
• Two approximations of solutions of Hamilton-Jacobi equations

  1984cited by this paper
• Contrôle impulsionnel et inéquations quasi variationnelles

  1982influential reference
• Annales de l'Institut Henri Poincaré

  1931cited by this paper

• GARCH-PDE Models for Option Pricing under Stochastic Volatility and Their Finite Difference Solvers

  2026cites this paper
• An efficient probabilistic scheme for the exit time probability of α-stable Lévy process

  2026cites this paper
• Two-productive sector equilibrium problems with heterogeneous agents under jump-diffusion models

  2026cites this paper
• Stochastic jump diffusion process informed neural networks for accurate American option pricing under data scarcity

  2025cites this paper
• A robust RBF-FD technique combined with polynomial enhancements for valuing European options in jump-diffusion frameworks

  2025influential citation
• Option pricing using the IMEX-AVF method with high jump intensity

  2025cites this paper
• Numerical valuation of European options under two-asset infinite-activity exponential Lévy models

  2025influential citation
• Going beyond the Black–Scholes option pricing model: Financial rogue waves in quantum mechanics

  2025cites this paper
• A stochastic Gordon-Loeb model for optimal cybersecurity investment under clustered attacks

  2025cites this paper
• Adaptive option pricing based on a posteriori error estimates for fully discrete finite difference methods

  2024cites this paper
• Enhancing valuation of variable annuities in Lévy models with stochastic interest rate

  2024cites this paper
• A simplified Wiener–Hopf factorization method for pricing double barrier options under Lévy processes

  2024influential citation
• Discretization of Fractional Fully Nonlinear Equations by Powers of Discrete Laplacians

  2024cites this paper
• Corporate debt value under transition scenario uncertainty

  2024cites this paper
• Fast Calculation of Integral Convolution Operators in Problems of Evaluating Options in Lévy’s Models

  2024cites this paper
• On a Schrödinger equation involving fractional (N/s1,q)-Laplacian with critical growth and Trudinger-Moser nonlinearity

  2024cites this paper
• Fourier Domain Physics Informed Neural Network

  2024cites this paper
• Generalized replicator dynamics based on mean-field pairwise comparison dynamic

  2024cites this paper
• RBF–based IMEX finite difference schemes for pricing option under liquidity switching

  2024cites this paper
• Probability of Default modelling with L\'evy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9

  2023influential citation
• Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models

  2023cites this paper
• Analysis of fractional differential equation and its application to realistic data

  2023cites this paper
• Error analysis of finite difference scheme for American option pricing under regime-switching with jumps

  2023cites this paper
• A de-singularized meshfree approach to default probability estimation under a regime-switching synchronous-jump tempered stable Lévy model

  2023cites this paper
• Temporal Difference Learning for High-Dimensional PIDEs with Jumps

  2023cites this paper
• Errors in the IMEX-BDF-OS methods for pricing American style options under the jump-diffusion model

  2023cites this paper
• Fast Q1 finite element for two-dimensional integral fractional Laplacian

  2023cites this paper
• Optimal error analysis of a non-uniform IMEX-L1 finite element method for time fractional PDEs and PIDEs

  2023influential citation
• Option Pricing for the Variance Gamma Model: A New Perspective

  2023cites this paper
• Fast Option Pricing using Nonlinear Stencils

  2023cites this paper
• An ETD method for multi‐asset American option pricing under jump‐diffusion model

  2023cites this paper
• American options pricing under regime-switching jump-diffusion models with meshfree finite point method

  2023cites this paper
• A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump

  2023cites this paper
• Fast American Option Pricing using Nonlinear Stencils

  2023cites this paper
• Precise Error Bounds for Numerical Approximations of Fractional HJB EInquations

  2023cites this paper
• Poisson Process Modeling of Pure Jump Equities on the Ghana Stock Exchange

  2022cites this paper
• Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance and Finance

  2022cites this paper
• A Posteriori Error Control and Adaptivity for the IMEX BDF2 Method for PIDEs with Application to Options Pricing Models

  2022cites this paper
• Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model

  2022cites this paper
• Numerical investigation of the variable-order fractional Sobolev equation with non-singular Mittag–Leffler kernel by finite difference and local discontinuous Galerkin methods

  2022cites this paper
• A second order numerical method for the time-fractional Black-Scholes European option pricing model

  2022cites this paper
• Valuation of variable annuities under stochastic volatility and stochastic jump intensity

  2022cites this paper
• A multidimensional Hilbert transform approach for barrier option pricing and survival probability calculation

  2022cites this paper
• Closed-form option pricing for exponential Lévy models: a residue approach

  2022cites this paper
• Stability analysis and error estimates of implicit–explicit Runge–Kutta local discontinuous Galerkin methods for nonlinear fractional convection–diffusion problems

  2022cites this paper
• JDOI variance reduction method and the pricing of American-style options

  2021cites this paper
• Dynamical behavior of a nonlocal Fokker-Planck equation for a stochastic system with tempered stable noise.

  2021cites this paper
• A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems

  2021cites this paper
• A trustable shape parameter in the kernel-based collocation method with application to pricing financial options

  2021cites this paper
• An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function

  2021cites this paper
• Computation of powered option prices under a general model for underlying asset dynamics

  2021cites this paper
• Cosine Willow Tree Structure under Lévy Processes with Application to Pricing Variance Derivatives

  2021cites this paper
• On Meshfree Collocation to Compute the Probability of Default under a Regime-Switching Synchronous-Jump Tempered Stable L\'{e}vy Model

  2021cites this paper
• Numerical valuation of European and American options under Merton's model

  2021cites this paper
• Option valuation under the VG process by a DG method

  2021cites this paper
• Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics

  2021cites this paper
• Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

  2021cites this paper
• On Numerical Solution of Structural model for the Probability of Default under a Regime-Switching Synchronous-Jump Tempered Stable Lévy Model with Desingularized Meshfree Collocation method

  2021cites this paper
• Deep Ritz method for the spectral fractional Laplacian equation using the Caffarelli-Silvestre extension

  2021cites this paper
• On solutions for fractional $$\pmb {N/s}$$-Laplacian equations involving exponential growth

  2021cites this paper
• Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality

  2021cites this paper
• Residue Sum Formula for Pricing Options under the Variance Gamma Model

  2021cites this paper
• Hamilton-Jacobi-Bellman-Isaacs equation for rational inattention in the long-run management of river environments under uncertainty

  2021cites this paper
• A Simple Wiener-Hopf Factorization Approach for Pricing Double-Barrier Options

  2021cites this paper
• A front-fixing ETD numerical method for solving jump-diffusion American option pricing problems

  2020cites this paper
• Optimal uniform error estimates for moving least‐squares collocation with application to option pricing under jump‐diffusion processes

  2020cites this paper
• Numerical Study of the Merton PIDE in Option Pricing

  2020cites this paper
• The Wiener-Hopf Factorization for Pricing Options Made Easy

  2020cites this paper
• An unsupervised deep learning approach to solving partial integro-differential equations

  2020cites this paper
• Optimal Investment, Heterogeneous Consumption and Best Time for Retirement

  2020cites this paper
• An extremely efficient numerical method for pricing options in the Black–Scholes model with jumps

  2020cites this paper
• On the pricing of multi-asset options under jump-diffusion processes using meshfree moving least-squares approximation

  2020cites this paper
• Technology adoption in a declining market

  2020cites this paper
• Fractional Partial Differential Equations Associated with Lêvy Stable Process

  2020cites this paper
• European rainbow option values under the two-asset Merton jump-diffusion model

  2020cites this paper
• A splitting strategy for the calibration of jump-diffusion models

  2020influential citation
• On finite difference schemes for partial integro-differential equations of Lévy type

  2020cites this paper
• Machine learning versus econometric jump models in predictability and domain adaptability of index options

  2019cites this paper
• Barycentric spectral domain decomposition methods for valuing a class of infinite activity Lévy models

  2019cites this paper
• Multiplicity results for fractional magnetic problems involving exponential growth

  2019cites this paper
• European Option Pricing of electricity under exponential functional of Lévy processes with Price-Cap principle

  2019cites this paper
• PRICING HOLDER-EXTENDABLE CALL OPTIONS WITH MEAN-REVERTING STOCHASTIC VOLATILITY

  2019cites this paper
• A parallel-in-time multigrid solver with a new two-level convergence for two-dimensional unsteady fractional Laplacian problems

  2019cites this paper
• Mapping of Barrier Option Pricing: A Co-citation Analysis

  2019cites this paper
• Finite Di ff erence Schemes for Linear Stochastic Integro-Di ff erential Equations

  2019cites this paper
• Numerical solutions of Black-Scholes integro-differential equations with convergence analysis

  2019cites this paper
• Investment valuation of natural tourist attractions under the uncertainty of multiple unexpected events: an ROV method

  2019cites this paper
• Efficient computation of european option prices and their sensitivities with the complex fourier series method

  2019cites this paper
• Multigrid method for pricing European options under the CGMY process

  2019cites this paper
• Stability of numerical methods under the regime-switching jump-diffusion model with variable coefficients

  2019cites this paper
• Operator splitting schemes for the two-asset Merton jump-diffusion model

  2019cites this paper
• Market making under a weakly consistent limit order book model

  2019cites this paper
• Three Essays on the Design, Pricing, and Hedging of Insurance Contracts

  2019cites this paper
• An IMEX‐BDF2 compact scheme for pricing options under regime‐switching jump‐diffusion models

  2019cites this paper
• Fast pricing of American options under variance gamma

  2019cites this paper
• DG Method for Pricing European Options under Merton Jump-Diffusion Model

  2019cites this paper
• Option pricing under a jump-telegraph diffusion model with jumps of random size

  2019cites this paper
• Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes

  2019cites this paper
• Computation of time–dependent implied volatility from point observations for European options under jump–diffusion models

  2019cites this paper
• Remarks on the Generalized Fractional Laplacian Operator

  2019cites this paper