An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients

作者：Chassagneux Jean Francois^*; Jacquier Antoine; Mihaylov Ivo

来源：SIAM Journal on Financial Mathematics, 2016, 7(1): 993-1021.

DOI：10.1137/15M1017788

• stochastic differential equations
• non-Lipschitz coefficients
• explicit Euler Maruyama scheme with projection
• CIR model
• Ait-Sahalia model
• multilevel Monte Carlo

We consider the approximation of one-dimensional stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler Maruyama discretization 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 to 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.

• 出版日期2016