Estimation On Mark To Market Risk Measure Under Strongly Mixing Dependence Structure

It is particularly important to measure market risk reasonably and accurately.However,most of the risk quantitative indicators with complete theory and extensive application,which are not suitable for capturing the potential risk of investment in any given day within a continuous trading period,are limited to one-day risk measure,and thus it is difficult to apply them to the assessment of internal risk of financial institutions with multiple settlements during the investment holding period.In order to make up for this defect,based on the mark to market value at risk(MMVaR),this dissertation further puts forward the mark to market conditional tail expectation(MMCTE),and gives the large sample properties of its empirical estimator under certain conditions.This dissertation mainly consists of the following three parts.In the first part,the empirical estimators of MMVaR and MMCTE are given,and their strong consistency and asymptotic normality theorems are derived on the premise that the time series satisfies the strictly stationary strongly mixing dependency assumption.The second part generates time series observations based on the ARMA(p,q)model satisfying the strictly stationary and strongly mixing conditions to explore the impact of the dependency structure and even the degree of dependency among time series observations,as well as the volatility of time series variable values,on the calculated values of MMVaR,VaR,MMCTE,and CTE,as well as the estimation effect of their empirical estimators.By stationary bootstrap,it is demonstrated that empirical estimators do perform well in estimating the aforementioned four risk measurement indexes through three indicators:average estimation bias,estimated standard error,and confidence interval.The third part includes two practical applications.Firstly,based on the daily trading data of 28 stock indexes collected from 2006 to 2020,this dissertation analyzes the possible reasons why the risk measurements,empirical estimates of each stock index vary with the year range,and clarifies the impact of the returns,volatility level on the empirical estimates of MMVaR,VaR,MMCTE,and CTE.Then,based on the daily yield data of Shanghai Composite Index,an investment early warning calculation with the rolling window method is carried out,to illustrate that MMCTE outperforms CTE in out-sample risk prediction assessment.Finally,for MMVaR,MMCTE and CTE,based on the daily yield data of 100 investment portfolios randomly constructed through 12 stocks,their empirical estimates for the same investment portfolio and among different investment portfolios are compared,and the impact of portfolio holding periods on their estimates is analyzed,so as to achieve the guidance on investing activities.