Copula Theory And Its Application In Financial Risk Management

The relationship between the financial markets is increasingly complex, as time goes on, the financial risk is becoming more and more complex, so a effective financial risk management is playing an increasingly important role. Copula is a useful tool in correlation analysis and multivariate statistical analysis, it can measure the dependence between assets efficiently, and it has the advantage at tail correlation analysis between financial market and VaR calculation. Most of the existing copulas are symmetric while data collected from the real world may exhibit asymmetric property, such as warranty claim data which exhibit unequal tail dependence in lower-upper and upper-lower. It is necessary to develop a asymmetric copula that can model this data, this paper offers the method to solve the problem. This paper is mainly divided into two parts, one part is about the theory of Copula, the other is about their application in financial risk management.The first part deeply discusses the theory knowledge of copula. We introduce some commonly used copulas, show their density function and distribution function plot to display their characters more intuitively. This part proposes a new constructing copulas method that differs from the other existing methods, which can construct the excellent copulas with more applications. The new copulas constructed in this paper are the derivative of the common copulas, which present not only the symmetric property, but also asymmetric property. We use some commonly-used copulas as base to construct the new copulas. In financial analysis, most financial data exhibit leptokurtosis, fat tails, asymmetric property, so the copulas constructed in this paper can handle the dependence more effectively.The second part contains the application of copula theory in Value at Risk of portfolios, as an example, taking the daily closing price of Shanghai Composite Index and Shenzhen Component Index as the object of study. In this part, we use the non-parametric kernel density to obtain the marginal distributions, estimate the copulas’ parameters with the help of Matlab. We also use Euclidean distance as the evaluation criteria and find t-copula can fit the data best than any other common copulas. After this, we use gaussian copula and t-copula as base copulas to construct the new copulas, which return to fit better than the commonly used copulas. At last, we calculate the Value at Risk of portfolios with different ratio by Monte Carlo Simulation to help the investors to choose a better portfolio.