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

See all articles by Lijun Bo

Lijun Bo

University of Science and Technology of China (USTC)

Xindan Li

Nanjing University

Yongjin Wang

Nankai University - Business School

Xuewei Yang

Nanjing University - School of Management and Engineering; Nanjing University - Institute of New Finance

Date Written: June 12, 2013

Abstract

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

Bo, Lijun and Li, Xindan and Wang, Yongjin and Yang, Xuewei, On the Conditional Default Probability in a Regulated Market with Jump Risk (June 12, 2013). Quantitative Finance, 13(12): 1967-1975, December 2013. , Available at SSRN: https://ssrn.com/abstract=2284631

Lijun Bo

University of Science and Technology of China (USTC) ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Xindan Li

Nanjing University ( email )

Nanjing, Jiangsu 210093
China

Yongjin Wang

Nankai University - Business School ( email )

94 Weijin Road, Nankai District
Tianjin, 300071
China

Xuewei Yang (Contact Author)

Nanjing University - School of Management and Engineering ( email )

22 Hankou Road, Gulou District
Nanjing, Jiangsu 210093
China

Nanjing University - Institute of New Finance ( email )

Nanjing, Jiangsu 210093
China

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