This paper empirically investigated the behavior of Korean CDS spread which captures the excess kurtosis and heavier tails (i.e. leptokurtic behavior). In capturing the dynamics of the Korean CDS spread, this study notably focuses on the comparison of mean reverting drifts and jump part of the continuous-time models of CDS spread. The results are as follows. First, Empirical findings indicate that the addition of jumps leads to a lower expected return (μ) and volatility (σ). This result implies that jumps account for a substantial portion of the overall volatility of the return data. Second, During Pre and Post Crisis period the GBM is better than competing models in terms of parameter significance, log-likelihood and the BIC. Third, the addition of jumps improves performance significantly since all jump diffusion processes outperform their diffusion counterparts especially during the crisis period. Finally, the addition of mean-reversion appears to increase the goodness-of-fit, especially in the case of the jump-diffusion models during the crisis period. Empirical findings are consistent with the descriptive analysis findings, namely the existence of jumps, the non-normality of returns and the non-stationarity of the price process.