||This thesis develops a market model with jump-diffusion dynamics for pricing portfolio credit derivatives. The state variables of the market model are mean loss rates, and the model can be calibrated to credit default swap rates quoted by market. The market model could be extended to incorporate either a Cox process where the default time is thought of the first jump time or the jump-diffusion process introduced by . With our arbitrage-free market model, the Black's formula for CDS option can be justified. By combining the market model with copula models of default times, we can price portfolio credit derivatives like CDOs, using Monte Carlo simulation. The implied base correlations are computed for different CDO equity tranches. In addition, some techniques for initial data processing and the possibility of adopting t-copula as a potential stochastic copula model have also been discussed.