Dependence modelling in insurance and finance using copulas - Xie, Wenjun (2017)
Understanding and quantifying dependence is at the core of all modelling efforts in the areas of insurance and finance. Insurance and financial variables are usually non-normal and have excessive skewness and kurtosis. Therefore, the conventional linear regression models may not be suitable to use in these cases. In this thesis, I introduce the use of the copula modelling technique in modelling the dependence in insurance and financial problems. A copula is an effective tool to model the joint distribution of random variables. The advantages of the copula modelling technique are twofold. First, it estimates the marginal distributions of each random variable separately, which removes the assumptions of normal marginal distributions at the beginning, and it can allow specifications of distributions with heavy tails. Second, it allows flexibility in choosing the functional form that best describes the dependency structure between cumulative densities of random variables. This enables us to not only investigate the linear associations but also any kind of non-linear associations. This thesis contains four studies. The first study discusses the use of copulas in a financial trading strategy, pairs trading. This study tries to generalize the pairs trading strategy using the copula technique to explicitly capture the marginal distributions as well as the dependency structure between the stock returns. The second study proposes a benchmark measurement of the loss ratio within a loss triangle using copulas to take consideration of dependency structure between different insurance business lines and discusses their implications on loss reserving. The third study proposes a copula-based residual bootstrapping procedure to deal with data paucity problem faced in cyber insurance pricing analysis. In the fourth study, I extend the current analysis into the multi-dimensional scenario. Current copula regression analysis is mainly restricted to two-dimension due to lack of choice of copulas at multi-dimension. In this study, I attempt to build a framework of multi-dimensional copula regression analysis using a non-parametric copula called Bernstein copula. It provides a closed-form solution and can be adapted to any dependency structure. I demonstrate the usefulness of the proposed method using two examples in insurance and finance.