Pricing credit default swaps with Parisian and Parasian default mechanics

Abstract

This paper proposes Parisian and Parasian default mechanics for modeling the credit risks of the CDS (credit default swap) contracts. Unlike most of the structural models used in the literature, our new model assumes that the default will occur only if the price of the reference asset stays below a certain level for a pre-described period of time. To work out the corresponding CDS price, a general pricing formula containing the unknown no-default probability is derived first. It is then shown that the determination of such a probability is equivalent to the valuation of a Parisian or Parasian down-and-out binary options, depending on how the time is recorded. After the option price is solved with a θ finite difference scheme, the CDS price is obtained through the derived general pricing formula. Finally, some numerical experiments are carried out to study the effects of the new default mechanics on the CDS prices.

KEYWORDS:

• Binary options
• credit default swaps
• finite difference method
• Parisian-type options

JEL code:

• G13

Acknowledgments

This work is supported by National Natural Science Foundation of China NO. 11601189, and Natural Science Foundation of Jiangsu Province NO. BK20160156. It is also supported by the Fundamental Research Funds for the central universities 2019JDZD16, and research base of humanities and social science outside Jiangsu universities “Research Center of Southern Jiangsu Capital Market” (2017ZSJD020).