Importance sampling and statistical Romberg method for Lévy processes

DOI10.1016/j.spa.2015.12.008zbMath1345.60044arXiv1408.0898OpenAlexW2286187608MaRDI QIDQ271865

Ahmed Kebaier, Mohamed Ben Alaya, Kaouther Hajji

Publication date: 20 April 2016

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.0898

zbMATH Keywords

Lévy processesMonte Carlo methodvariance reductioncentral limit theoremsCGMY modelEsscher transformstatistical Romberg method

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Numerical methods (including Monte Carlo methods) (91G60) Central limit and other weak theorems (60F05) Monte Carlo methods (65C05) Stochastic approximation (62L20)

Related Items (3)

New methods of simulating Lévy processes ⋮ Central limit theorem for the antithetic multilevel Monte Carlo method ⋮ Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions
• Multilevel Monte Carlo for Lévy-driven SDEs: central limit theorems for adaptive Euler schemes
• Jump-adapted discretization schemes for Lévy-driven SDEs
• Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes
• Tempering stable processes
• Importance sampling and statistical Romberg method
• The Euler scheme for Lévy driven stochastic differential equations
• Central limit theorem for the multilevel Monte Carlo Euler method
• Optimal posting price of limit orders: learning by trading
• Monte Carlo option pricing for tempered stable (CGMY) processes
• The approximate Euler method for Lévy driven stochastic differential equations
• Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing
• Approximations of small jumps of Lévy processes with a view towards simulation
• Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options
• Connecting discrete and continuous lookback or hindsight options in exponential Lévy models
• Multilevel Monte Carlo Path Simulation
• Financial Modelling with Jump Processes
• Adaptative Monte Carlo Method, A Variance Reduction Technique
• Error Bounds for Small Jumps of Lévy Processes
• Optimal Importance Sampling Parameter Search for Lévy Processes via Stochastic Approximation
• Multilevel Path Simulation for Jump-Diffusion SDEs
• Continuity Correction for Barrier Options in Jump-Diffusion Models
• Expansion of the global error for numerical schemes solving stochastic differential equations

This page was built for publication: Importance sampling and statistical Romberg method for Lévy processes