Analytical Solution for Expected Loss of a Collateralized Loan: A Square-root Intensity Process Negatively Correlated with Collateral Value
In this study, we derive an explicit solution for the expected loss of a collateralized loan, focusing on the negative correlation between default intensity and collateral value. Three requirements for the default intensity and the collateral value are imposed. First, the default event can happen at any time until loan maturity according to an exogenous stochastic process of default intensity. Second, default intensity and collateral value are negatively correlated. Third, the default intensity and collateral value are non-negative. To develop an explicit solution, we propose a square-root process for default intensity and an affine diffusion process for collateral value. Given these settings, we derive an explicit solution for the integrand of the expected recovery value within an extended affine model. From the derived solution, we find the expected recovery value is given by a Stieltjes integral with a measure-changed survival probability.
|Date of creation:||Jun 2010|
|Contact details of provider:|| Postal: 2-1-1 Nihonbashi, Hongoku-cho, Chuo-ku, Tokyo 103|
Web page: http://www.imes.boj.or.jp/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Long Chen & Pierre Collin-Dufresne & Robert S. Goldstein, 2009. "On the Relation Between the Credit Spread Puzzle and the Equity Premium Puzzle," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3367-3409, September.
- Hui Chen & Scott Joslin, 2012.
"Generalized Transform Analysis of Affine Processes and Applications in Finance,"
Review of Financial Studies,
Society for Financial Studies, vol. 25(7), pages 2225-2256.
- Hui Chen & Scott Joslin, 2011. "Generalized Transform Analysis of Affine Processes and Applications in Finance," NBER Working Papers 16906, National Bureau of Economic Research, Inc.
- Xin Guo & Robert A. Jarrow & Yan Zeng, 2009. "Modeling The Recovery Rate In A Reduced Form Model," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 73-97. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:ime:imedps:10-e-10. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Kinken)
If references are entirely missing, you can add them using this form.