[Jens Kroeske]

Let me clarify what I meant by ‘loosely defined term’; In the PRM handbook it is mentioned (III.B.3.1) that ‘in practice many simplifications are used when exposure amounts are estimated’. And later on (III.B.3.3) it says with regards to fixed coupon bonds that ‘A common approximation is to set the exposure constant until maturity’. All this, I think, refers to how ‘exposure is actually handled in practice.

The FRM handbook is actually a bit more precise and defines ‘current exposure’ as Max(PV,0). It also discusses ‘potential exposure’ which can only be estimated given an assumption about the distribution of underlying risk factors. Both would have to be estimated by the institution (rather than being strictly defined).

Therefore I personally would answer your question in the following manner:

1. The current exposure is the current market value, i.e. 96USD at the time of purchase and a best guess at the market value at any time between purchase and maturity.
2. The potential exposure depends on the how you would model the relevant interest rate and the confidence.
3. In practice institutions would probably get away with saying that the exposure is simply the notional amount + accrued.

Anything more sophisticated sounds to me like spurious accuracy given the large uncertainly in other parameters (PD, LGD), but I accept that this is of little help in an exam.

[Jens Kroeske]

http://en.wikipedia.org/wiki/Taylor_series

[Jens Kroeske]

I think you need to distinguish between ‘legal claim amount’ (what you claim for in a bankruptcy court) and the somewhat loosely defined notion of ‘exposure’. For a bond, the legal claim amount is the notional amount plus accrued interest (see PRM Handbook III.B.2.6). Exposure should ideally be the replacement value (i.e. what you get in the market for it), which might not always be easy to determine and which might be substantially different from the legal claim amount.

With regards to your second question my guess would be that it depends on whether the bank intends to hold the bond to maturity or whether it intends to actively trade it.

Hope this helps

[Jens Kroeske]

The Macaulay duration of a consol is (1+y)/y = 1+1/y (where y is the yield) as you rightly derived. I think the questions asks for the Modified duration which is (Macaulay duration)/(1+y) = 1/y (which is actually easier to derive using the fact that PV = coupon/yield* FV, taking the derivative with respect to the yield y and dividing by -PV).

Hope this helps

[Jens Kroeske]

Z is a standard normal random variable, i.e. mean zero and variance one.
P(Z > 2) = 1 – P(Z<=2) = 1 - NORMSDIST(2) = 0.022750132 (using excel, for example)

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