Canonical least-squares Monte Carlo valuation of American options: convergence and empirical pricing analysis
type: Item
instance of: scholarly article
title: Canonical least-squares Monte Carlo valuation of American options: convergence and empirical pricing analysis
zbMATH Open document ID: 1407.91280
DOI: 10.1155/2014/763751
author: Xisheng Yu
author: Qiang Liu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The paper by \textit{Q. Liu} [``Pricing American options by canonical least-squares Monte Carlo'', J. Futures Mark. 30, No. 2, 175--187 (2010)] introduces a method termed the canonical least-squares Monte Carlo (CLM) which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S\&P 100 Index (OEX) puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 7017218
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/763751
OpenAlex ID: W1993728783
Wikidata QID: Q59072036
cites work: Valuing American Options by Simulation: A Simple Least-Squares Approach
cites work: Pricing American options using a nonparametric entropy approach
cites work: An analysis of a least squares regression method for American option pricing
cites work: American options with stochastic dividends and volatility: a nonparametric investigation
cites work: Nonparametric estimation of American options' exercise boundaries and call prices
cites work: The Entropic Penalty Approach to Stochastic Programming
cites work: Numerical Methods in Finance and Economics
cites work: Q4794126
cites work: Option pricing: A simplified approach
description: scientific article; zbMATH DE number 7017218