基于程式化模型与梯度信息随机克里金法的风险测度估计  

Estimating risk measures via stochastic Kriging with stylized model and gradient information

作　　者：蔡小婷 云昕 姜广鑫 CAI Xiaoting;YUN Xin;JIANG Guangxin(School of Management Science and Engineering,Dongbei University of Finance and Economics,Dalian 116025,China;School of Management,Shanghai University,Shanghai 200444,China;SILC Business School,Shanghai University,Shanghai 200444,China;School of Management,Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]东北财经大学管理科学与工程学院,大连116025 [2]上海大学管理学院,上海200444 [3]上海大学悉尼工商学院,上海200444 [4]哈尔滨工业大学经济与管理学院,哈尔滨150001

出　　处：《系统工程理论与实践》2022年第10期2657-2676,共20页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(72171060,72121001,71801148)。

摘　　要：嵌套仿真是估计金融衍生产品投资组合风险测度的常用方法,但是其仿真计算量大,运算效率较低.本文提出了基于程式化模型的随机克里金法(stochastic Kriging,SK)来对投资组合损失函数进行拟合,替代大量的内层仿真,从而提高运算效率.在此基础上,本文进一步提出了两种方式将梯度信息引入到基于程式化模型的SK方法,即直接利用梯度信息嵌入到SK中和利用梯度信息进行插值,后者对于程式化模型的选择具有更高的灵活性.本文利用极大似然估计的渐进正态性,进一步建立了在有梯度信息条件下验证程式化模型有效性的统计假设检验方法.最后,通过基于几何布朗运动的欧式期权、亚式期权,基于正态逆高斯过程的欧式期权,以及包含多类期权的投资组合的例子,验证所提出的SK方法的有效性,结果表明带有程式化模型和梯度信息的SK方法可以提高估计的精度,提高运算效率.Nested simulation is commonly used in estimating the risk measures of a portfolio with financial derivatives.But nested simulation requires a large number of simulation budgets and has low computational efficiency.This paper proposes a new method,i.e.,the stochastic Kriging(SK)with stylized model,to fit the loss function of the portfolio instead of a large number of inner simulation budgets in the nested simulation,thereby improving computational efficiency.Moreover,we propose two ways to embed gradient information into SK with stylized model,i.e.,embedding the gradient information directly into SK and using gradient information for interpolation.The latter is more flexible in choosing the stylized model.By the asymptotic normality of the maximum likelihood estimation,this paper derives a statistical hypothesis test to evaluate the effectiveness of the stylized model with gradient information.In the numerical experiments,we use examples of European options and Asian options based on geometric Brownian motion,European options based on the normal inverse Gaussian process,and portfolio with multiple options to verify the effectiveness of the proposed methods.The results show that the SK method with stylized models and gradient information can improve estimation accuracy and increase computation efficiency.

关 键 词：蒙特卡罗方法 风险度量 随机克里金法 嵌套仿真 随机梯度估计 

分 类 号：F830.9[经济管理—金融学]