Basket Credit Derivative Pricing in a Markov Chain Model with Interacting Intensities

Kangquan Zhi,Xiaosong Qian,Jie Guo,Wenguang Yu

doi:10.1155/2020/5369879

Abstract

In this paper, we propose a Markov chain model to price basket credit default swap (BCDS) and basket credit-linked note (BCLN) with counterparty and contagion risks. Suppose that the default intensity processes of reference entities and the counterparty are driven by a common external shock as well as defaults of other names in the contracts. The stochastic intensity of the external shock is a Cox process with jumps. We derive recursive formulas for the joint distribution of default times and obtain closed-form premium rates for BCDS and BCLN. Numerical experiments are performed to show how the correlated default risks may affect the premium rates.

Highlights

E conditional independence approach assumes that the default intensities are conditionally independent under the given filtration, see Wang and Garleanu [5], Giesecke [6], and Liang et al [7]
We focus on the pricing of basket credit derivatives (BCDS and basket credit-linked notes (BCLN))
Inspired by Leung and Kwok [22], we present a more general model to study basket credit derivatives with interacting default intensities, which are driven by an external shock as well as defaults of other names in the contracts

Summary

Markov Chain Model with Interacting Intensities

For the cases that k reference entities default, the corresponding states of Ht are HRM and HRM ∪ S for M ⊂ I and |M| k, where |M| is the cardinal number of set M. e corresponding elements in the infinitesimal generator matrix Λ[ψS](t) are as follows:. In the HRM -column of the generator matrix Λ[ψS](t), the positive elements represent the transition intensities from other states to state HRM by one jump. In the HRM ∪ S-row of the generator matrix Λ[ψS](t), the positive elements represent the transition intensities from state HRM ∪ S to other states by one jump. In the HRM∪ S-column of the generator matrix Λ[ψS](t), the positive elements represent the transition intensities from other states to state HRM∪ S by one jump. Replacing the conditional expectations in (29) with equation (31), we obtain the unconditional transition probabilities

Pricing Basket Credit Derivatives

Numerical Analysis

Conclusion