In this thesis, a copula model is constructed to estimate dependency and calculate the Value at Risk for insurance coverage under the dependence of the covered losses. The dependence model is illustrated in a three-dimensional setting to simplify the complex theoretical functions and provide an accessible introduction to the copula model. The modeling uses the U.S. crop insurance dataset aggregated by each county level and commodity type. The composite likelihood approach helps to simplify the computation in high-dimensional problems by approximating the negative log-likelihood using bivariate components. In this study, the majorization-minimization principle is employed to estimate the parameters of the normal copula by minimizing the composite likelihood iteratively. To avoid overfitting and result in a valid correlation matrix, the L1 penalty is applied to induce sparsity and shrink irrelevant parameters toward zero. The optimal tuning parameter is selected based on the BIC score to generate a positive semi-definite correlation matrix for the result. In the Appendix of the thesis, the dependence model is extended to a high dimension. The Value at Risk computed for the fictional insurance contract in the data analysis results in a higher value when considering dependence between variables.
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