论文标题
插值漂移隐式Euler MLMC方法用于屏障选项定价以及应用于CIR和CEV模型
Interpolated Drift Implicit Euler MLMC Method for Barrier Option Pricing and application to CIR and CEV Models
论文作者
论文摘要
最近，Giles等人。 [14]证明，多层次蒙特卡洛（MLMC）方法在扩散过程中评估向下和障碍选项的效率$（x_t）_ {t \ in [0，t]} $具有全球lipschitz系数的效率，可以通过结合棕色的桥梁技术和条件的蒙特罗方法来改进，以改进$ \ inf_ {t \ in [0，t]} x_t $在屏障附近具有有界密度。在目前的工作中，借助Lamperti转换技术，并使用了Alfonsi的漂移隐式Euler方案的Brownian插值[2]，我们表明，在某些时刻构造下，也可以提高MLMC的效率，以评估具有非LIPSCHITZ扩散系数的模型的障碍选项。我们研究了两个示例模型：Cox-Ingersoll-Ross（CIR）和方差弹性（CEV）过程的常数，我们表明，在模型参数的某些限制下，我们的理论框架条件得到了满足。特别是，我们为运行最小值的密度和CIR和CEV工艺的最大运行最大运行而开发了半明确的公式，这些公式具有独立感兴趣。最后，处理数值测试以说明我们的结果。
Recently, Giles et al. [14] proved that the efficiency of the Multilevel Monte Carlo (MLMC) method for evaluating Down-and-Out barrier options for a diffusion process $(X_t)_{t\in[0,T]}$ with globally Lipschitz coefficients, can be improved by combining a Brownian bridge technique and a conditional Monte Carlo method provided that the running minimum $\inf_{t\in[0,T]}X_t$ has a bounded density in the vicinity of the barrier. In the present work, thanks to the Lamperti transformation technique and using a Brownian interpolation of the drift implicit Euler scheme of Alfonsi [2], we show that the efficiency of the MLMC can be also improved for the evaluation of barrier options for models with non-Lipschitz diffusion coefficients under certain moment constraints. We study two example models: the Cox-Ingersoll-Ross (CIR) and the Constant of Elasticity of Variance (CEV) processes for which we show that the conditions of our theoretical framework are satisfied under certain restrictions on the models parameters. In particular, we develop semi-explicit formulas for the densities of the running minimum and running maximum of both CIR and CEV processes which are of independent interest. Finally, numerical tests are processed to illustrate our results.
