Market prices of corporate bond spreads and of credit default swap (CDS) rates do not match each other. In this paper, we argue that the liquidity premium, the cheapest-to-deliver (CTD) option and actual market segmentation explain the pricing differences. Using the European transaction data from Reuters and Bloomberg, we estimate a liquidity premium that is time-varying and firm-specific. We show that when time-dependent liquidity premiums are considered, corporate bond spreads and CDS rates behave in a much closer way than previous studies have shown. We also find that high equity volatility drives pricing differences that can be explained by the CTD option.