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An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients

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Title: An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients
Authors: Chassagneux, JFC
Jacquier, A
Mihyalov, IM
Item Type: Journal Article
Abstract: We consider the approximation of one-dimensional stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modi- fied explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the optimal strong error rate. We apply this scheme to SDEs widely used in the mathematical finance literature, including the Cox-Ingersoll-Ross (CIR), the 3/2 and the Ait-Sahalia models, as well as a family of mean-reverting processes with locally smooth coefficients. We numerically illustrate the strong convergence of the scheme and demonstrate its efficiency in a multilevel Monte Carlo setting.
Issue Date: 14-Dec-2016
Date of Acceptance: 29-Aug-2016
URI: http://hdl.handle.net/10044/1/29871
DOI: 10.1137/15M1017788
ISSN: 1945-497X
Publisher: Society for Industrial and Applied Mathematics
Start Page: 993
End Page: 1021
Journal / Book Title: SIAM Journal on Financial Mathematics
Volume: 7
Issue: 1
Replaces: 10044/1/39923
http://hdl.handle.net/10044/1/39923
Copyright Statement: © 2016, Society for Industrial and Applied Mathematics
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M008436/1
Keywords: Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
stochastic differential equations
non-Lipschitz coefficients
explicit Euler Maruyama scheme with projection
CIR model
Ait-Sahalia model
multilevel Monte Carlo
STOCHASTIC DIFFERENTIAL-EQUATIONS
MULTILEVEL MONTE-CARLO
OPTIONS
APPROXIMATIONS
TIME
Computational finance
Numerical analysis
q-fin.CP
q-fin.CP
math.NA
60H10
0102 Applied Mathematics
0104 Statistics
1502 Banking, Finance and Investment
Publication Status: Published
Online Publication Date: 2016-12-14
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences