Nth CDS Monte Carlo Pricing under Stochastic Recovery Rates

Recovery rates play an important role in Nth CDS pricing, while, it's difficult to get realistic recovery rates. Assuming that the recovery rates are stochastic and follow different Copulas with corresponding default times. Under this assumption, we develop a simulation Algorithm to price the Nth CDS. According to the result of simulation pricing, the prices of Nth CDS are different under the condition of constant recovery rates, stochastic independent recovery rates and Copula structure recovery rates.