On the Conditional Default Probability in a Regulated Market with Jump Risk
Quantitative Finance, 13(12): 1967-1975, December 2013.
17 Pages Posted: 26 Jun 2013 Last revised: 14 Jun 2017
Date Written: June 12, 2013
In this paper, we introduce tractable dynamic models for financial variables (such as interest rates, foreign exchange rates, commodity prices, etc.) with capturing both jump risk and boundedness of the price fluctuation in a regulated market. For the jump risk, we use a compound Poisson process with double exponential jump amplitude to describe the jumps. As for the boundedness of the fluctuation, we introduce two regulators to regulate (or control) the price dynamics. Based on such a dynamics, we then study the default events under the structural framework for credit risk. The explicit expression for the Laplace transform of the default time is derived. For exploring the effect of the jump risk and the regulation, we perform some numerical simulation. As a practical application, an analytic valuation of defaultable zero-coupon bonds is presented. It turns out that our model can produce a variety of strictly positive credit spread term structures, including downward, humped and upward styles.
Keywords: Conditional default probability, Defaultable bond, Credit spread, Regulated market, Regulated jump-diffusions
JEL Classification: G12, G10
Suggested Citation: Suggested Citation