Multilevel Monte Carlo for exponential Lévy models

DOI10.1007/s00780-017-0341-7zbMath1403.91371arXiv1403.5309OpenAlexW1559531285WikidataQ59613327 ScholiaQ59613327MaRDI QIDQ2412390

Michael B. Giles, Yuan Xia

Publication date: 23 October 2017

Published in: Finance and Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5309

zbMATH Keywords

Asian options\(\alpha\)-stable processmultilevel Monte Carloexponential Lévy modelsbarrier optionsnormal inverse Gaussian processlookback optionsvariance Gamma processconvergence discretely sampled running maximum

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Gaussian processes (60G15) Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items (11)

A multidimensional Hilbert transform approach for barrier option pricing and survival probability calculation ⋮ Geometrically Convergent Simulation of the Extrema of Lévy Processes ⋮ Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation ⋮ A Monte Carlo algorithm for the extrema of tempered stable processes ⋮ Zooming-in on a Lévy process: failure to observe threshold exceedance over a dense grid ⋮ Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing ⋮ Superposition, reduction of multivariable problems, and approximation ⋮ Implementable coupling of Lévy process and Brownian motion ⋮ Discretization error for a two-sided reflected Lévy process ⋮ General multilevel Monte Carlo methods for pricing discretely monitored Asian options ⋮ On the strong convergence rate for the Euler-Maruyama scheme of one-dimensional SDEs with irregular diffusion coefficient and local time

Cites Work

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• On the asymptotic behavior of the density of the supremum of Lévy processes
• Suprema of Lévy processes
• On the law of the supremum of Lévy processes
• Small-time asymptotics of stopped Lévy bridges and simulation schemes with controlled bias
• On extrema of stable processes
• A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations
• Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction
• A Wiener-Hopf Monte Carlo simulation technique for Lévy processes
• On irregular functionals of SDEs and the Euler scheme
• Discretization error in simulation of one-dimensional reflecting Brownian motion
• Multilevel Monte Carlo simulation for Lévy processes based on the Wiener-Hopf factorisation
• Introductory lectures on fluctuations of Lévy processes with applications.
• Multilevel Monte Carlo Methods
• On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process
• Connecting discrete and continuous lookback or hindsight options in exponential Lévy models
• A Combinatorial Lemma and Its Application to Probability Theory
• Multilevel Monte Carlo Path Simulation
• A Method for Simulating Stable Random Variables
• Financial Modelling with Jump Processes

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