ﺳﻨﺠﺶ رﻳﺴﻚ ﺷﺎﺧﺺ ﮔﺮوه ﺑﺎﻧﻜﻲ ﺑﺎ اﺳﺘﻔﺎده از ﺗﺨﻤﻴﻦ ﻧﻮﺳﺎﻧﺎت ﺑﺎزده ﺑﺎ ﻣﺪل ﻧﻮﺳﺎﻧﺎت ﺗﺼﺎدﻓﻲ: روﻳﻜﺮد ﻧﻴﻤﻪ ﭘﺎراﻣﺘﺮي ﺑﻴﺰي

Risk Evaluation of Banking Index with Volatility Estimation through Stochastic Volatility Model: A Semiparametric Bayesian Approach

ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻛﺎرﺑﺮد ﺗﻮزﻳﻊ ﺑﺎزدﻫﻲ در ﻣﺤﺎﺳﺒﺔ ﻣﻌﻴﺎرﻫﺎي رﻳﺴﻚ و واﺑﺴﺘﮕﻲ دﻗﺖ ﺗﺨﻤﻴﻦ اﻳﻦ ﻣﻌﻴﺎرﻫﺎ ﺑﻪ ﺻﺤﺖ ﺗﻮزﻳﻊ ﺑﺎزده، ﺑﺮآورد ﺻﺤﻴﺢ آن ﻫﻤﻮاره در ﻛﺎﻧﻮن ﺗﻮﺟﻪ ﭘﮋوﻫﺸـﮕﺮان ﺑـﻮده اﺳﺖ. ﺑﺎ وﺟﻮدي ﻛﻪ اﺳﺘﻔﺎده از ﻣﺪل ﭘﺎراﻣﺘﺮي ﻧﻮﺳﺎﻧﺎت ﺗﺼﺎدﻓﻲ ﺑﻪﻣﻨﻈﻮر ﺗﺨﻤﻴﻦ ﻧﻮﺳـﺎﻧﺎت ﺑـﺎزده در ﻣﻄﺎﻟﻌﺎت ﭘﻴﺸﻴﻦ ﻣﺘﺪاول اﺳﺖ، ﻓﺮض ﻣﺬﻛﻮر اﻏﻠﺐ ﺑﻪ ﻧﺘﺎﻳﺠﻲ ﺑﺎ دﻗﺖ ﻛﺎﻓﻲ ﻣﻨﺠـﺮ ﻧﻤـﻲ ﺷـﻮد ﺑﻨﺎﺑﺮاﻳﻦ در اﻳﻦ ﺗﺤﻘﻴﻖ ﺑﺮﺧﻼف ﻓﺮض ﻣﻌﻤﻮل ﭘﺎراﻣﺘﺮي ﺑﻮدن ﺗﻮزﻳـﻊ ﺟﻤـﻼت اﺧـﻼل در ﻣـﺪل ﻧﻮﺳﺎﻧﺎت ﺗﺼﺎدﻓﻲ، ﺑﺎ ﺑﻬﺮه ﮔﻴﺮي از روﻳﻜﺮد ﻧﻴﻤـﻪ ﭘـﺎراﻣﺘﺮي ﺑﻴـﺰي ، ﺑـﻪ ﺗﺨﻤـﻴﻦ ﺟﻤـﻼت اﺧـﻼل ﭘﺮداﺧﺘﻪ ﺷﺪه اﺳﺖ. در ﭘـﮋوﻫﺶ ﺣﺎﺿـﺮ ﺗﻮزﻳـﻊ ﻟﮕـﺎرﻳﺘﻢ ﻣﺮﺑـﻊ ﺑـﺎزده ﺷـﺎﺧﺺ ﮔـﺮوه ﺑـﺎﻧﻜﻲ ﺑـﺎ ﺑﻪ ﻛﺎرﮔﻴﺮي آﻣﻴﺨﺘﻪ اي از ﺗﻮزﻳﻊ ﻫﺎي ﺧﺎﻧﻮادة ﻧﺮﻣﺎل و ﺑﺎ اﺳـﺘﻔﺎده از زﻧﺠﻴـﺮ ة ﻣـﺎرﻛﻒ ﻣﻮﻧـﺖ ﻛـﺎرﻟﻮ ﻣﺪل ﺳﺎزي ﺷﺪ و در ﻧﻬﺎﻳﺖ ﻧﺘﺎﻳﺞ آن ﺑﺎ ﻣﺪل ﻧﻮﺳﺎﻧﺎت ﺗﺼﺎدﻓﻲ ﻧﺮﻣﺎل، ﻣﻘﺎﻳﺴﻪ ﮔﺮدﻳﺪ. ﻧﺘـﺎﻳﺞ اﻳـﻦ ﺑﺮرﺳﻲ ﻧﺸﺎن ﻣﻲ دﻫﺪ، در ﻣﻮاﻗﻌﻲ ﻛـﻪ ﺗﻮزﻳـﻊ ﺑـﺎزده داراي ﭼـﻮﻟﮕﻲ ﺑﺎﺷـﺪ، ﻣـﺪل ﻧﻴﻤـﻪ ﭘـﺎراﻣﺘﺮي ﻧﻮﺳﺎﻧﺎت را دﻗﻴﻖ ﺗﺮ ﺗﺨﻤﻴﻦ ﻣﻲ زﻧﺪ، ﺿﻤﻦ آن ﻛﻪ در ﺷﺮاﻳﻄﻲ ﻛﻪ ﺗﻮزﻳﻊ ﺑـﺎ زده ﺑـﻪ ﺗﻮزﻳـﻊ ﻧﺮﻣـﺎل ﻧﺰدﻳﻚ ﺑﺎﺷﺪ، ﻧﺘﺎﻳﺞ ﻣﺪل ﺣﺎﺿﺮ، ﻣﺸﺎﺑﻪ ﻧﺘﺎﻳﺞ ﻣﺪل ﻧﻴﻤﻪﭘﺎراﻣﺘﺮي ﺑﺎ ﻓﺮض ﺗﻮزﻳﻊ ﻧﺮﻣﺎل ﺧﻮاﻫﺪ ﺑﻮد.

Estimation of the return distribution has a crucial role in Risk measurement and since the precision of risk measures depends on the precision of the return distribution, truly estimation of return distribution has attracted a huge attention. Although using Stochastic Volatility models with parametric assumptions for estimation and illustration of the volatilities has been common in research, these assumptions usually result in careless estimations. So in the following research a semiparametric approach has been used for estimation of the volatility by using a normal mixture dirichlet process. In this paper the distribution of the logarithm of the squared returns of banking index of Tehran Stock Exchange has been estimated by using mixtures of normal family and employing an MCMC algorithm. Finally, the results has been compared to the Basic stochastic volatility model. The results show that when the return distribution is skewed, estimates of volatility using the model can differ dramatically from those using a Normal return distribution. Furthermore, when return distribution is similar to a normal distribution, the results of this model are similar to the results of the parametric model.