A second-order discretization with Malliavin weight and Quasi-Monte Carlo method for option pricing. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Yamada, Toshihiro; Yamamoto, Kenta
• Is Part Of: Quantitative finance. Volume 20:Issue 11(2020)
• Page Start: 1825
• Page End: 1837
• Publication Date: 2020-11-01
• Subjects: Option pricing -- European option -- Digital option -- Quasi-Monte Carlo method -- SABR model -- Weak approximation -- Stochastic differential equations -- Malliavin calculus; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2018.1430371
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : This paper shows a second-order discretization scheme for expectations of stochastic differential equations. We introduce a smart Malliavin weight which is given by a sum of simple polynomials of Brownian motions as an improvement of the scheme of Yamada [ J. Comput. Appl. Math., 2017, 321, 427–447]. A new quasi-Monte Carlo simulation is proposed to obtain an efficient option pricing scheme. Numerical examples for the SABR model are shown to illustrate the validity of the scheme.