Abstract
This paper discusses the pricing problem of credit default swap in the fractional Brownian motion environment. As credit default swap is exposed to both the interest rate risk and the default risk, we assume that the default intensity of a firm depends on the stochastic interest rate and the default states of counterparty firms. The interest rate risk is reflected by the fractional Vasicek interest rate model. We model the firm’s default intensity under the looping default model and derive the pricing formulas of risky bonds and credit default swap.
Highlights
Credit risk is one of the main risks in the financial industry. It is very important for the financial industry to manage credit risk effectively
We consider that the source of credit risk may be from the issuer of bond and the seller of credit default swap (CDS)
Firm A is the primary party whose default only depends on the risk-free interest rate and the firm B is the secondary party whose default depends on the interest rate and the default state of firm A ; Case 3
Summary
Credit risk is one of the main risks in the financial industry. It is very important for the financial industry to manage credit risk effectively. The default-free bond’s price was obtained in [11] as following: Theorem 2 ([11]) Let P t, T be the time-t value of the default-free bond with the maturity date T. In recent years, [16,17] further allowed the stochastic interest rate to follow an jump-diffusion process and studied the pricing problem of bonds and CDS in details. Based on the obtained conclusions, we will price the bonds and CDS with the fractional Vasicek interest rate in the looping default framework. Theorem 4 Assume the interest rate follows the fractional Vasicek model and the default intensities tA and tB satisfy (7) and (8). The pricing formula (14) of bond issued by firm A can be derived though the similar proving process of.
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