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

By Rama Cont, Ekaterina Voltchkova. SIAM Journal on Numerical Analysis, 2005

472 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Finance, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5265a62ca82cc5037dceeb77eb8a7c2a6d121347

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Citations in the corpus

Robust numerical valuation of European and American options under the CGMY process (2007, methodology): “For the integral over Ω0, we use a similar approach as in [14] in approximating the integral of ν(y) by a finite process with an effective diffusion coefficient.”
On American Options Under the Variance Gamma Process (2007, methodology): “A discussion of the degenerate case (purely jump processes, like the VG process) for European options is provided in Cont and Voltchkova (2005), where the concept of viscosity solution is used to obtain existence and uniqueness results under rather weak conditions. For the degenerate case a classica”
Numerical solution of two asset jump diffusion models for option valuation (2008, methodology): “Using a different localization technique, the bounds for this error in one dimension were estimated in [12] using a probabilistic approach.”
Jump‐Diffusion Models (2010, unknown): “Equation (5) is a partial integro-differential equation (PIDE) which can be solved using finite difference methods [2].”
Jump-diffusion Models: a Practitioner's Guide (2009, background): “A complete presentation with proofs, as well as the general case of possibly infinite Lévy measure, can be found in [23, 12].”
Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes (2007, methodology): “Despite this simplicity and unlike the Black-Scholes model, closed option pricing formulas are not available in exponential Lévy models and one must use either deterministic numerical methods (partial integro-differential equations [8] or Fourier methods [4]) or Monte Carlo methods which form the ob”
Pricing Path-Dependent Options with Jump Risk via Laplace Transforms (2005, methodology): “Numerical solutions based on solving partial integro-differential equations are given in Cont and Voltchkova (2005) and d’Haullin et al. (2003).”
Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering (2007, methodology): “For example, I will omit numerical solutions for jump-diffusion models; see Cont and Tankov (2004), Cont and Voltchkova (2005) and d’Halluin et al. (2003) on numerical methods for solving partial integro-differential equations, and Feng and Linetsky (2005) and Feng et al. (2004) on how to price…”
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, methodology): “The observation that the Wiener–Hopf factorization and related first-passage distributions are tractable for a random walk in the case where the jump distribution on the positive half-axis follows an exponential distribution can already be found in Feller (1971). See also the books of Borovkov (1976”