14688

1400 دكتري

دكتري

رياضي كاربردي (مالي)

اصفهان : دانشگاه صنعتي اصفهان

1398

نه، 92 ص. : مصور، جدول، نمودار

محمدتقي جهانديده

مهديه طهماسبي

بيژن ظهوري زنگنه، ندا اسماعيلي

1398/03/29

كتابنامه

رياضي

رياضي

1398/03/29

2542378

Weak Multilevel Monte Carlo Method and its Application in Financial Derivative Pricing Azadeh Ghasemifard azadeh ghasemi@math iut ac ir May 2019 PhD Thesis in Persian Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Mohammad Taghi Jahandideh jahandid@cc iut ac irAdvisor Dr Mahdieh Tahmasebi tahmasebi@modares ac ir2010 MSC 65C30 65C05 60H10 91G80 Keywords multilevel Monte Carlo method stochastic differential equation weak approximation schemes option pricing 1 Abstract Asset value is a stochastic process whose dynamics is modeled by a stochastic differential equation Given the specific features of an asset this equation can be continuous or with jumps Considering thepossibility of lacking an analytical solution or the difficulty of calculating it we need to be able to estimatethe solution numerically in order to know the financial derivative price at any given moment A financialderivative is a tool based on the value of an underlying asset such as bonds and it is effective for reducingthe risk of investment To price a financial derivative we need to compute an expected value In this the sis we consider the multilevel Monte Carlo method for calculating the expected value of an underlyingasset as E f Xt where f is the payoff function of the financial derivative For this purpose we studythe numerical solution of the stochastic differential equation in diffusion and jump diffusion models andestimate the expected value using the weak multilevel Monte Carlo method Note that the following three papers are the results of this thesis work 1 Debrabant K Ghasemifard A and Mattson C N Weak antithetic MLMC estimation of SDEswith the Milstein scheme for low dimensional Wiener processes Applied Mathematics Letters 91 22 27 2019 2 Ghasemifard A Jahandideh M Multilevel Monte Carlo Simulation Applied to L vy driven As sets Mathematical Researches Persian submitted 3 Tahmasebi M Ghasemifard A Jahandideh M Comments on Strong convergence rates forbackward Euler on a class of nonlinear jump diffusion problems Journal of Computational and AppliedMathematics 205 949 956 2007 Journal of Computational and Applied Mathematics 359 69 72 2019

محمدتقي جهانديده

مهديه طهماسبي

بيژن ظهوري زنگنه، ندا اسماعيلي