統計学輪講（第２５回）

統計学輪講（第25回）
日時      2014年01月14日(火)    15時40分～16時30分
場所      経済学部新棟３階第３教室
講演者    朴　海香 (経済M2)
演題      Realized Cholesky Stochastic Volatility Model

概要
Multivariate stochastic volatility has many important applications in finance, 
including asset pricing and risk management, but it is not easy to estimate. 
One of the reasons is because for $p$ time series, there are $p(p+1)/2$ elements 
we need to estimate. The second reason is that the covariance matrix must to be 
positive definite for all time point. In this paper, we use Cholesky decomposition 
to solve the positiveness problem. First, we decompose covariance matrix by 
Cholesky decomposition to ensure the positivity of the covariance matrix. Second, 
we introduce realized covariance matrix and construct the Realized Cholesky Stochastic 
Volatility (RCSV) model to make model more accurate.  Moreover, we propose priors and 
we estimate variables and parameters by Bayesian approach. At the end of the paper, 
we apply our approach to stocks' price data and construct portfolios by using 
the estimated parameters. We compare the variance of our portfolio returns with 
that of a simple model that ignores  the correlation between stocks.