@article{Chassagneux:2016:10.1137/15M1017788,
author = {Chassagneux, JFC and Jacquier, A and Mihyalov, IM},
doi = {10.1137/15M1017788},
journal = {SIAM Journal on Financial Mathematics},
pages = {993--1021},
title = {An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients},
url = {http://dx.doi.org/10.1137/15M1017788},
volume = {7},
year = {2016}
}

Download

TY  - JOUR
AB  - 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 strongconvergence, with a rate. Under some regularity and integrability conditions, weobtain the optimal strong error rate. We apply this scheme to SDEs widely usedin the mathematical finance literature, including the Cox-Ingersoll-Ross (CIR), the3/2 and the Ait-Sahalia models, as well as a family of mean-reverting processeswith locally smooth coefficients. We numerically illustrate the strong convergenceof the scheme and demonstrate its efficiency in a multilevel Monte Carlo setting.
AU  - Chassagneux,JFC
AU  - Jacquier,A
AU  - Mihyalov,IM
DO  - 10.1137/15M1017788
EP  - 1021
PY  - 2016///
SN  - 1945-497X
SP  - 993
TI  - An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients
T2  - SIAM Journal on Financial Mathematics
UR  - http://dx.doi.org/10.1137/15M1017788
UR  - http://arxiv.org/abs/1405.3561v3
UR  - http://hdl.handle.net/10044/1/29871
VL  - 7
ER  - 

Download