Abstract
This paper provides a methodology for valuing a credit default swap (CDS) with considering a counterparty default risk. Using a structural framework, we study the correlation of the reference entity and the counterparty through the joint distribution of them. The default event discussed in our model is associated to whether the minimum value of the companies in stochastic processes has reached their thresholds (default barriers). The joint probability of minimums of correlated Brownian motions solves the backward Kolmogorov equation, which is a two dimensional partial differential equation. A closed pricing formula is obtained. Numerical methodology, parameter analysis and calculation examples are implemented.
Highlights
A vanilla credit default swap (CDS) is a kind of insurance against credit risk
This paper provides a methodology for valuing a credit default swap (CDS) with considering a counterparty default risk
If there is no credit event occurs during the term of the swap, the buyer continues to pay the premium until the CDS maturity
Summary
A vanilla credit default swap (CDS) is a kind of insurance against credit risk. The buyer of the CDS is the buyer of protection who pays a fixed fee or premium to the seller of protection for a period of time. They extended their study to the situation where there is possibility of counterparty default risk and obtained a pricing formula with Monte Carlo simulation [11]. The valuation of the credit default swap is based on computing the joint default probability of the reference entity and the counterparty (protection seller). It is difficult because correlation between the entities involved in the contract is hard to deal with. Jarrow and Yildirim [12] obtained a closed form valuation formula for a CDS based on reduced form approach with correlated credit risk In their model, the default intensity is assumed to be linear in the short interest rate.
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