Contingent convertible bonds (CoCos) are hybrid instruments characterized by both debt and equity. CoCos are automatically converted into equity or written down when a predefined trigger event occurs. The present study quantifies the issuing bank's default risk that only manifests in the post-conversion period for pricing CoCos depending on a loss-absorbing method. This work aims to reflect the distinct features of equity-conversion CoCos - in contrast to a write-down CoCos - in a valuation framework. Accordingly, we propose a model to compute the ratio of common equity Tier 1 (CET1), which is composed of core capital and risky assets, by employing a geometric Brownian motion and a random variable. Then, we formulate the post-conversion risk premium by measuring the probability with which the bank's CET1 ratio breaches a regulatory default threshold after conversion. Finally, we empirically examine a positive value of the post-conversion risk premium embedded in the market prices of equity-conversion CoCos.