Efficient simulations in the t-Copula model of supply portfolio risk considering breach of contract probabilities

We consider two different risks for a supply portfolio namely market risk (changes in the spot market price of the commodity exchanged in supply chain contracts) and breach of contract risk (related to the supplier defaults) simultaneously in a copula-based model. As it is quite subtle to model this common dependence structure, we use two independent t-copula dependence structures for market and breach of contract risks. An efficient simulation algorithm integrating conditional Monte Carlo and importance sampling based on cross-entropy is proposed for quantifying the risk measure supply-at-risk (SaR) under the proposed model. Numerical results for a realistic commodity metal portfolio demonstrates the value of the proposed ecient simulation algorithm.