This paper develops a kaleckian economy in a stock-flow consistent (SFC) model to assess the effect of contingent convertible bonds (CoCos) in terms of stability through numerical simulations. The specific characteristics of the model are a dual sector of households (workers and investors) and a dual banking system (retail banks and investment banks). Two simulations are implemented. One focuses on an increase in defaults on workers' loans which triggers a write-down of CoCos issued by retail banks and the other on a decrease in corporate share prices which triggers a write-down of CoCos issued by investment banks. The overall effects are qualitatively similar. There is a shift of risks and adjustment costs from issuers to holders of CoCos which reduces companies' investment and investing-households’ consumption. The simulations show that the triggering of CoCos has a positive effect on the balance sheet of CoCos issuers. It also reduces the cost of bailouts. In return, there is an increase in real and financial instability. Two regulatory recommendations follow from this research. (1) Banks could be required to issue a fraction of their debt in CoCos in order to reduce bailout costs. (2) When CoCos are activated, their issuer could be forced not to intervene on all or part of the financial markets, for a predefined period of time and/or value, in order to limit the destabilisation of price assets.