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According to Gregory, the exposure for. the long party of a credit default swap increases in its early years and then skyrockets when there is a credit event of the reference entity.

I would have suspected the exposure starts off negative and then skyrockets when there is a credit event.

Is this behaviour related to the theory that default probabilities increase with time?

In case I misunderstood (I don't think I did), here is the source text

Consider the exposure profile of a single-name CDS as shown in Figure 8.20 (long CDS protection). The exposure increases in the early stages, which corresponds to scenarios in which the CDS premium (credit spread) will have widened. However, the maximum exposure on the CDS corresponds to the reference entity experiencing a credit event, which triggers an immediate payment of the notional less a recovery value

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The value of a long protection CDS is the value of the protection leg minus the value of the premium leg. As time goes, the premium leg value decreases since the # of premium payments reduces. However, the protection leg value will increase because of the survival probability reduces while the LGD is held the same.The exposure, which is the positive port of the CDS value, will then increase.

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First, one needs a definition of exposure. I believe in this case the author is referring to PFE. If you are long CDS, you are paying premiums to receive protection from default. When default occurs, you receive a payout, and the value of your CDS contract is at a maximum. By definition of PFE, the exposure is at a maximum.

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