We derive the optimal credit default swap premium a financial institution requires to assume the
default risk of fixed income instruments. This premium is a function of the institution’s capital
and current exposure. In most cases, an institution requires an increasing premium to assume
additional risk. However, we show that an under-capitalized institution that already has
substantial default risk exposure would engage in risk-shifting and assume more risk at lower
rates. In other words, the presence of a financial institution with large default risk exposure in the
market reduces the premium required to insure additional risk. Therefore, negative signals about
the default risk of the debt instruments may vastly increases the quantity of insured instruments
with no effect on insurance premium. In fact, default insurance premiums decline in the face of
increasing demand. Consistent with this, prior to the recent financial crisis, the credit default
swap issuance increased greatly, as did the volume of the underlying nontraditional mortgages,
but the data suggests that required premiums stayed constant or declined.
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