Valuation of Loan Credit Default Swaps Correlated Prepayment and Default Risks with Stochastic Recovery Rate

In this paper, we establish an intensity based multi-factor model to value LCDS. The pricing model incorporates the modeling of default, prepayment and recovery risks. Using one factor model, negative correlation between the default and prepayment intensities and positive correlation between the default intensity and the loss given default are described. The interest rate and the house price are chosen as the relevant factors. Under these assumption, a Cauthy problem of PDE is derived, which has a closed-form solution. Based on the solution, numerical examples are provided.