Journal of Credit Risk

Analytical solutions for the expected loss of a collateralized loan: a square root intensity process negatively correlated with collateral value

Satoshi Yamashita and ToshinaoYoshiba


This paper analytically evaluates the expected loss and the nth moment of the loss distribution for a collateralized loan by focusing on the negative correlation between default intensity and collateral value. To ensure a negative correlation and nonnegativity of intensity, we propose a square root process for default intensity and a negatively correlated affine diffusion process for collateral value. Given these settings, we derive an explicit solution for the integrand of the expected recovery value and the kth moment of the recovery value, using measure-changed survival probabilities. Finally, we analyze the expected loss and standard deviation of the loss based on the estimation of parameters for default intensity and the collateral value process.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here