An ADI Sparse Grid method for Pricing Efficiently American Options under the Heston Model

作     者：A.Clevenhaus M.Ehrhardt M.Gunther 

作者机构：Institute of Mathematical ModellingAnalysis and Computational Mathematics(IMACM)Chair of Applied Mathematics and Numerical AnalysisBergische Universitat WuppertalGaußstraße 2042119 WuppertalGermany 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2021年第13卷第6期

页      面：1384-1397页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the bilateral German-Slovakian Project MATTHIAS–Modelling and Approximation Tools and Techniques for Hamilton-Jacobi-Bellman equations in finance and Innovative Approach to their Solution financed by DAAD and the Slovakian Ministry of Education.Further the authors acknowledge partial support from the bilateral German-Portuguese Project FRACTAL–FRActional models and CompuTationAL Finance financed by DAAD and the CRUP–Conselho de Reitores das Universidades Portuguesas 

主　　题：Sparse grid combination technique American options ADI Heston model 

摘      要：One goal of financial research is to determine fair prices on the financial *** financial models and the data sets on which they are based are becoming ever larger and thus more complex,financial instruments must be further developed to adapt to the new complexity,with short runtimes and efficient use of memory *** we show the effects of combining known strategies and incorporating new ideas to further improve numerical techniques in computational *** this paper we combine an ADI(alternating direction implicit)scheme for the temporal discretization with a sparse grid approach and the combination *** later approach considerably reduces the number of“spatialgrid *** presented standard financial problem for the valuation of American options using the Heston model is chosen to illustrate the advantages of our approach,since it can easily be adapted to other more complex models.