Quantitative error estimates for a least-squares Monte Carlo algorithm for American option pricing

DOI10.1007/s00780-013-0204-9zbMath1282.91380OpenAlexW1998129102MaRDI QIDQ354190

Daniel Z. Zanger

Publication date: 18 July 2013

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

Full work available at URL: https://doi.org/10.1007/s00780-013-0204-9

zbMATH Keywords

dynamic programmingAmerican optionsstatistical learningleast-squares Monte CarloLongstaff-Schwartz algorithm

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) General nonlinear regression (62J02) Monte Carlo methods (65C05) Dynamic programming (90C39) Financial applications of other theories (91G80) Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items (19)

ESTIMATING RESIDUAL HEDGING RISK WITH LEAST-SQUARES MONTE CARLO ⋮ Sequential Design for Optimal Stopping Problems ⋮ Regression-Based Complexity Reduction of the Nested Monte Carlo Methods ⋮ On fair designs of c<scp>ross‐chain</scp> exchange for cryptocurrencies via Monte Carlo simulation ⋮ An improved least squares Monte Carlo valuation method based on heteroscedasticity ⋮ Unbiased optimal stopping via the MUSE ⋮ Primal-Dual Regression Approach for Markov Decision Processes with General State and Action Spaces ⋮ Discrete-type approximations for non-Markovian optimal stopping problems. II ⋮ CONVERGENCE OF A LEAST‐SQUARES MONTE CARLO ALGORITHM FOR AMERICAN OPTION PRICING WITH DEPENDENT SAMPLE DATA ⋮ On the convergence of the quasi-regression method: polynomial chaos and regularity ⋮ AMERICAN OPTION PRICING WITH REGRESSION: CONVERGENCE ANALYSIS ⋮ Pricing bounds and bang-bang analysis of the Polaris variable annuities ⋮ Optimal Stopping of McKean--Vlasov Diffusions via Regression on Particle Systems ⋮ General Error Estimates for the Longstaff–Schwartz Least-Squares Monte Carlo Algorithm ⋮ Implied stopping rules for American basket options from Markovian projection ⋮ Pricing Bermudan Options via Multilevel Approximation Methods ⋮ Dynamic programming for optimal stopping via pseudo-regression ⋮ Distribution-free robust linear regression ⋮ The difference between LSMC and replicating portfolio in insurance liability modeling

Uses Software

• ElemStatLearn

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The longstaff-Schwartz algorithm for Lévy models: results on fast and slow convergence
• Monte Carlo algorithms for optimal stopping and statistical learning
• Assessing the least squares Monte-Carlo approach to American option valuation
• Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
• On the degree of approximation by manifolds of finite pseudo-dimension
• An analysis of a least squares regression method for American option pricing
• Number of paths versus number of basis functions in American option pricing
• A distribution-free theory of nonparametric regression
• A forward scheme for backward SDEs
• A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options
• A regression-based Monte Carlo method to solve backward stochastic differential equations
• A Review on Regression-based Monte Carlo Methods for Pricing American Options
• Convergence of a Least‐Squares Monte Carlo Algorithm for Bounded Approximating Sets
• PRICING OF HIGH-DIMENSIONAL AMERICAN OPTIONS BY NEURAL NETWORKS
• Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives
• Neural Network Learning
• Valuing American Options by Simulation: A Simple Least-Squares Approach
• The elements of statistical learning. Data mining, inference, and prediction

This page was built for publication: Quantitative error estimates for a least-squares Monte Carlo algorithm for American option pricing