In this paper, we review recent advances in pricing tranches of a collateralized debt obligations and credit default swap indexes: one factor Gaussian copula model and its extensions, the structural model, and the loss process model. Then, we propose using heavy-tailed functions in future research. As background, we provide a brief explanation of collateralized debt obligations, credit default ...

A flip-swap language is a set \(\mathbf{S}\) of binary strings length n such that \(\mathbf{S} \cup \{0^n\}\) closed under two operations (when applicable): (1) Flip the leftmost 1; and (2) Swap 1 with bit to its right. Flip-swap languages model many combinatorial objects including necklaces, Lyndon words, prefix normal left factors k-ary Dyck feasible solutions 0-1 knapsack problems. We prove ...

Given two n-bit (cyclic) binary strings, A and B, represented on a circle (necklace instances). Let each sequence have the same number k of 1’s. We are interested in computing the cyclic swap distance between A and B, i.e., the minimum number of swaps needed to convert A to B, minimized over all rotations of B. We show that, given the compressed representation of A and B, this distance may be c...

Using the reduced form framework with inter-dependent default correlation, we perform valuation of credit default swap with counterparty risk. The inter-dependent default risk structure between the protection buyer, protection seller and the reference entity in a credit default swap are characterized by their correlated default intensities, where the default intensity of one party increases whe...