ﮐﺎرﺑﺮد ﻣﺪل ﺣﺮﮐﺖ ﺑﺮاووﻧﯽ ﻫﻨﺪﺳﯽ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﺗﻮﺳﻂ ﻓﺮآﯾﻨﺪ رژﯾﻢ ﺳﻮﺋﯿﭽﯿﻨﮓ ﻣﺎرﮐﻮف درﺷﺒﯿﻪ ﺳﺎزي ﻗﯿﻤﺖ ﺳﻬﺎم: روﯾﮑﺮد ﭘﻮﯾﺎﯾﯽ ﺷﻨﺎﺳﯽ ﺳﯿﺴﺘﻤﯽ

Application of Generalized Geometric Bravoni Motion Model by Markov Switching Regime Process in Stock Price Simulation: System Dynamics Approach

در اﯾﻦ ﭘﮋوﻫﺶ ﺗﻐﯿﯿﺮات ﻗﯿﻤﺖ ﺳﻬﺎم ﺷﺮﮐﺖ اﯾﺮان ﺧﻮدرو ﭘﺬﯾﺮﻓﺘﻪ ﺷﺪه در ﺑﻮرس اوراق ﺑﻬﺎدار ﺗﻬﺮان در دوره زﻣﺎﻧﯽ 1387/9/23 اﻟﯽ 1396/12/13 ﺑﺎ ﻫﺪف ﻣﺪل ﺳﺎزي، ﺑﺮ اﺳﺎس ﻣﺪل ﺣﺮﮐﺖ ﺑﺮاووﻧﯽ ﻫﻨﺪﺳﯽ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﺑﺎﻓﺮآﯾﻨﺪرژﯾﻢ ﺳﻮﺋﯿﭽﯿﻨﮓ ﻣﺎرﮐﻮف ﮐﻪ ﺷﮑﻞ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﻣﺪل ﺣﺮﮐﺖ ﺑﺮاووﻧﯽ ﻫﻨﺪﺳﯽ ﻣﯽ ﺑﺎﺷﺪ، ﺑﺮروي ﻣﻘﻮﻟﻪ ﭘﯿﺶ ﺑﯿﻨﯽ ﻣﻮرد ﻣﻄﺎﻟﻌﻪ ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ. ﻣﺪل ﭘﮋوﻫﺶ ﺑﺎ اﺳﺘﻔﺎده از روﯾﮑﺮد ﭘﻮﯾﺎﯾﯽ ﺷﻨﺎﺳﯽ ﺳﯿﺴﺘﻤﯽ و ﻧﺮم اﻓﺰار Vensim DSS اﺑﺘﺪا در ﻗﺎﻟﺐ ﻧﻤﻮدار ﻋﻠﯽ-ﻣﻌﻠﻮﻟﯽ و ﭘﺲ از ﻣﺸﺨﺺ ﻧﻤﻮدن ﻣﺘﻐﯿﺮﻫﺎي ﺣﺎﻟﺖ و ﺟﺮﯾﺎن، درﻗﺎﻟﺐ ﻧﻤﻮدارﺣﺎﻟﺖ و ﺟﺮﯾﺎن ﺗﮏ ﺣﻠﻘﻪاي و دو ﺣﻠﻘﻪاي ﻃﺮاﺣﯽ وﺷﺒﯿﻪ ﺳﺎزي ﺑﺮاي ﻗﯿﻤﺖ ﭘﺎﯾﺎﻧﯽ روزاﻧﻪ ﺳﻬﺎم اﻧﺠﺎم ﮔﺮﻓﺖ. دو ﭘﺎراﻣﺘﺮ رﯾﺸﻪ اﺧﺘﻼل و ﮔﺎم زﻣﺎﻧﯽ ﺑﻪ ﻋﻨﻮان ﭘﺎراﻣﺘﺮﻫﺎي ﺗﺤﻠﯿﻞ ﺣﺴﺎﺳﯿﺖ ﺷﻨﺎﺳﺎﯾﯽ و ﺑﮑﺎرﮔﺮﻓﺘﻪ ﺷﺪ. اﺑﺘﺪا ﺧﻄﺎي ﺷﺒﯿﻪ ﺳﺎزي ﺑﻪ ازاي ﺗﻐﯿﯿﺮات ﺗﺼﺎدﻓﯽ در رﯾﺸﻪ اﺧﺘﻼل 22/74 درﺻﺪ و درﮔﺎم زﻣﺎﻧﯽ 30/35 درﺻﺪ ﺑﺮآورد ﺷﺪ. ﺑﻌﻠﺖ ﺑﺎﻻ ﺑﻮدن ﺧﻄﺎي ﺷﺒﯿﻪ ﺳﺎزي ﺑﺎﻻﺗﺮ از ﺣﺪ ﻗﺎﺑﻞ ﻗﺒﻮل 15درﺻﺪ، ﻫﺮ دو ﭘﺎراﻣﺘﺮﮐﺎﻟﯿﺒﺮه ﺷﺪﻧﺪ. ﺟﻬﺖ ﺗﺨﻤﯿﻦ ﻣﻨﺎﺳﺒﯽ از ﻣﺤﺪوده ﭘﺎراﻣﺘﺮﻫﺎي ﮐﺎﻟﯿﺒﺮاﺳﯿﻮن ازروش آزﻣﻮن وﺧﻄﺎ و ﻣﺸﺎﻫﺪه ﻣﯿﺪاﻧﯽ رﻓﺘﺎرﺳﯿﺴﺘﻢ اﺳﺘﻔﺎده ﮔﺮدﯾﺪ. ﺧﻄﺎي ﺷﺒﯿﻪ ﺳﺎزي ﭘﺲ ازﮐﺎﻟﯿﺒﺮاﺳﯿﻮن ﺑﻪ ازاي ﭘﺎراﻣﺘﺮ رﯾﺸﻪ اﺧﺘﻼل از 22/74 درﺻﺪ ﺑﻪ 8/5 درﺻﺪ و ﺑﻪ ازاي ﮔﺎم زﻣﺎﻧﯽ از 30/35 درﺻﺪ ﺑﻪ 3/63 درﺻﺪ ﮐﺎﻫﺶ ﯾﺎﻓﺖ. دﻗﺖ ﺷﺒﯿﻪ ﺳﺎزي ﺑﻪ ازاي ﭘﺎراﻣﺘﺮ رﯾﺸﻪ اﺧﺘﻼل از77/26 درﺻﺪ ﺑﻪ 91/5 درﺻﺪ و ﺑﻪ ازاي ﮔﺎم زﻣﺎﻧﯽ از 69/65 درﺻﺪ ﺑﻪ 96/37 درﺻﺪ اﻓﺰاﯾﺶ ﯾﺎﻓﺖ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽدﻫﺪ ﺑﺎﺑﻬﯿﻨﻪ ﺳﺎزي ﭘﺎراﻣﺘﺮﻫﺎي ﮐﺎﻟﯿﺒﺮاﺳﯿﻮن ﻣﯿﺰان رﯾﺸﻪﻫﺎي ﺧﻄﺎ ﺑﻪ ﺣﺎﻟﺖ اﯾﺪه آل رﺳﯿﺪه ﯾﻌﻨﯽ ﺧﻄﺎي ﻧﺎﺑﺮاﺑﺮي ﮐﻮوارﯾﺎﻧﺲﻫﺎ ﺑﻪ ﺳﻤﺖ ﻋﺪد ﯾﮏ و ﺧﻄﺎي ﻧﺎﺑﺮاﺑﺮي ﻣﺒﻨﺎ و ﺧﻄﺎي ﻧﺎﺑﺮﺑﺮي وارﯾﺎﻧﺲﻫﺎ ﺑﻪ ﺳﻤﺖ ﻋﺪد ﺻﻔﺮ ﻧﺰدﯾﮏ ﺷﺪه وﻧﺸﺎن از ﺻﺤﺖ ﻋﻤﻠﮑﺮد ﻣﺪل ﭘﮋوﻫﺶ در ﺷﺒﯿﻪ ﺳﺎزي 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.