Abstract
In this paper, we intend to establish the PIDE pricing model of interest rate swap with default risk under Variance Gamma process. Under the assumption of the dynamics assets price process of a counterparty with Variance Gamma (VG) process, we treat the assets price process as a direct variable in the partial integro-differential equation (PIDE) of interest rate swap pricing, different from the working paper, in which they treat the default risk calculated from the Variance Gamma process as an item of the adjustment interest rate. At the end of this paper, we give a numerical result from the PIDE and find that a one hundred basis point of credit spread (bond spread) only results in 0.115 basis point in swap spread.
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