Abstract
In this paper, we explore mutual information based stock networks to build regular vine copula structure on high frequency log returns of stocks and use it for the estimation of Value at Risk (VaR) of a portfolio of stocks. Our model is a data driven model that learns from a high frequency time series data of log returns of top 50 stocks listed on the National Stock Exchange (NSE) in India for the year 2014. The Ljung-Box test revealed the presence of Autocorrelation as well as Heteroscedasticity in the underlying time series data. Analysing the goodness of fit of a number of variants of the GARCH model on each working day of the year 2014, that is, 229 days in all, it was observed that ARMA(1,1)-EGARCH(1,1) demonstrated the best fit. The joint probability distribution of the portfolio is computed by constructed an R-Vine copula structure on the data with the mutual information guided minimum spanning tree as the key building block. The joint PDF is then fed into the Monte-Carlo simulation procedure to compute the VaR. If we replace the mutual information by the Kendall's Tau in the construction of the R-Vine copula structure, the resulting VaR estimations were found to be inferior suggesting the presence of non-linear relationships among stock returns.
Highlights
Developing multivariate models and estimating joint density function is an area of key interest amongst researchers in finance and in various other fields [1,2,3]
This paper demonstrates the power of incorporating mutual information based metrics into the construction of R-vine copula structures in learning the joint distribution of a large
The data considered in the present analysis has an instant-by-instant record of transactions of 89 stocks listed on the National Stock Exchange (NSE) of India in the year 2014
Summary
Developing multivariate models and estimating joint density function is an area of key interest amongst researchers in finance and in various other fields [1,2,3]. The researchers have already discarded multivariate Gaussian distributions on log returns of stocks and developing methods to estimate the joint distribution of stock returns have always attracted lot of interest [4]. In this paper we use Copula functions to achieve the important goal of estimating the joint probability distribution of the portfolio. We need to overcome two challenges: firstly, to identify the probability distributions of the individual stocks and secondly devise a computationally efficient method of combining these marginal distributions with an appropriate.
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