Abstract
This paper mainly discusses the pricing of credit default swap (CDS) in the fractional dimension environment. We assume that the default intensity of a firm depends on the default states of counterparty firms and the term structure of interest rates, but the contagious impact of the counterparty firm is decreasing over time, until disappears. The interest rate risk is reflected by the fractional Vasicek interest rate model. We model the firm’s default intensity in the looping default framework and derive the pricing formulas of risky bonds and credit default swap.
Highlights
Credit default swap was one of the most important derivatives in the financial market, which was created by JP Morgan in 1995 to manage credit risk
As the fractional Brownian motion has the properties of self-similarity and long-range dependence and many phenomena in financial market show these properties in some certain, the fractional Brownian motion becomes a very suitable tool in different applications such as mathematical finance
This paper studies the pricing of the defaultable bonds and credit default swap when contagious risk has the attenuation effect in the fractional dimension environment
Summary
Credit default swap was one of the most important derivatives in the financial market, which was created by JP Morgan in 1995 to manage credit risk. Later, motivated by a series of events such as the South Korean banking crisis, Long Term Capital Management’s potential default and so on, [5] thought the traditionally structural and reduced-form models were full of problems because they all ignored the firm’s specific source of credit risk. They generalized the Davis’s contagion model and introduced the concept of counterparty risk which was from the default of firm’s counterparties. Based on the previous studies, this paper will establish the attenuation model of the contagious risk and deduce the pricing formula of credit default swap in the fractional dimension environment
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