We analyze the effect of counterparty risk on insurance contracts using the case of credit risk transfer in banking. In addition to the familiar moral hazard problem caused by the insuree's ability to influence the probability of a claim, this paper uncovers a new moral hazard problem on the other side of the market. We show that the insurer's investment strategy may not be in the best interests of the insuree. The reason for this is that if the insurer believes it is unlikely that a claim will be made, it is advantageous for them to invest in assets which earn higher returns, but may not be readily available if needed. This paper models both of these moral hazard problems in a unified framework. We find that instability in the insurer can create an incentive for the insuree to reveal superior information about the risk of their "investment". In particular, a unique separating equilibrium may exist even in the absence of any signalling device. We extend the model and show that increasing the number of insurers with which the insuree contracts can exacerbate the moral hazard problem and may not decrease counterparty risk. Our research suggests that regulators should be wary of risk being offloaded to other, possibly unstable parties, especially in newer financial markets such as that of credit derivatives.