کاربرد مدل حرکت براوونی هندسی تعمیم یافته توسط فرآیند رژیم سوئیچینگ مارکوف درشبیه سازی قیمت سهام: رویکرد پویایی شناسی سیستمی
محورهای موضوعی : مهندسی مالی
ناهید مالکی نیا
1
(گروه حسابداری و مدیریت ، واحد بیله سوار، دانشگاه آزاد اسلامی بیله سوار ، ایران)
حسین عسگری آلوج
2
(گروه حسابداری و مدیریت، واحد بیله سوار، دانشگاه آزاد اسلامی ، بیله سوار ، ایران)
ظاهر سپهریان
3
(گروه ریاضی ، واحد بیله سوار، دانشگاه آزاد اسلامی ، بیله سوار ، ایران)
کلید واژه: کالیبراسیون, پویایی شناسی سیستم, حرکت براوونی هندسی, رانش, رژیم سوئیچینگ مارکوف,
چکیده مقاله :
هدف:دراین پژوهش تغییرات قیمت سهام شرکت ایران خودروپذیرفته شده در بورس اوراق بهادار تهران دردوره زمانی 23/9/1387 الی 13/12/1396 با هدف مدل سازی، بر اساس مدل حرکت براوونی هندسی تعمیم یافته بافرآیندرژیم سوئیچینگ مارکوف که شکل تعمیم یافته مدل حرکت براوونی هندسی می باشد، برروی مقوله پیش بینی مورد مطالعه قرار گرفته است.روش: مدل پژوهش بااستفاده ازرویکردپویایی شناسی سیستمی ونرم افزار Vensim DSS ابتدادرقالب نمودارعلی-معلولی و پس ازمشخص نمودن متغیرهای حالت وجریان، درقالب نمودارحالت وجریان تک حلقه ای ودوحلقه ای طراحی وشبیه سازی برای قیمت پایانی روزانه سهام انجام گرفت.دوپارامترریشه اختلال وگام زمانی به عنوان پارامترهای تحلیل حساسیت شناسایی وبکار‌گرفته شد. یافته ها: ابتدا خطای شبیه سازی به ازای تغییرات تصادفی درریشه اختلال 74/22 درصد و درگام زمانی 35/30 درصد برآوردشد. بعلت بالابودن خطای شبیه سازی بالاترازحدقابل قبول 15درصد، هردوپارامترکالیبره شدند. جهت تخمین مناسبی از محدوده پارامترهای کالیبراسیون ازروش آزمون وخطا و مشاهده میدانی رفتارسیستم استفاده گردید. خطای شبیه سازی پس ازکالیبراسیون به ازای پارامترریشه اختلال از 74/22 درصد به 5/8 درصد وبه ازای گام زمانی از 35/30 درصد به 63/3 درصد کاهش یافت. دقت شبیه سازی به ازای پارامترریشه اختلال از26/77 درصد به 5/91 درصد و به ازای گام زمانی از 65/69 درصد به 37/96درصد افزایش یافت.نتیجه گیری: نتایج‌نشان‌می‌دهد بابهینه سازی پارامترهای کالیبراسیون میزان ریشه های خطا به حالت ایده آل رسیده یعنی خطای نابرابری کوواریانس هابه سمت عدد یک و خطای نابرابری مبنا وخطای نابربری واریانس ها به سمت عدد صفر نزدیک شده ونشان ازصحت عملکردمدل پژوهش‌درشبیه سازی قیمت سهام دارد.
Objective: In this study, the changes of the stock price of Iran Khodro Company listed in Tehran Stock Exchange (TSE) has been studied on the issue of prediction modeling during of 9/13/1387 to 13/12/1396 based on Geometric Brownian Motion (GBM) model generalized by the Markov switching regime (MSR).Methods: The research model was designed by system dynamics (SD) approach and Vensim DSS software in the causal- loop diagrams (CLD) firstly and then after specifying the flow-state variables, mono-loop and two-loop stock–flow diagrams (SFDs) was designed and daily final stock price was simulated. Two-parameter of noise seed and time step were identified and applied as sensitivity analysis parameters.Results: The simulation error was estimated for the random variations of the noise seed and the time step configured by default user parameters up to 22/74 and 30/35 percent, respectively. Both parameters were calibirated due to higher simulation error than acceptable error of 15 percent. Trial - error and field observation methods was performed in order to appropriate estimation of the calibration parameters range.The post-calibration accuracy of simulation per noise seed parameter increased from 77/26 to 91/5 percent and per time step from 69/65 to 96/37 percent.Conclusion: Findings indicate that the error roots have reached to the ideal mode by optimizing of the calibration parameters as covariance inequality error approached to one unit and base inequality error and variance inequality error approached to zero and indicate functionality accuracy of the GBM generalized by the MSR in stock price simulation.
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