CreditMetrics Bond Pricing [Saunders p. 337]

[mikey10011]

I'm going through Saunders p. 337 on CreditMetrics and the use of *forward* rates doesn't seem to jive with slide 22 of Market B.

It seems to me that Saunder's r1, r2, etc. should be *spot* rates [slide 21] rather than *forward* rates.

Note that de Servigny also talks about *forward* rates on p. 221.

For original source see CreditMetrics Technical Document:
See also http://www.ma.hw.ac.uk/~mcneil/F79CR/CMTD1.pdf [Acrobat p. 39]

 

[mikey10011]

In addition to Saunder p. 337 he repeats the calculation in Eq. 4.12 in Linda Allen et. al p. 140-1.

 

[mikey10011]

Using your notation in slide 21, Market B, could Saunders be talking about the *forward* rates f(1,2), f(1,3), f(1,4), f(1,5) [which would be the *spot* rates 1 year from now]?

 

[David Harper CFA FRM]

Mikey,

That is interesting; a great example of where i feel the generic notion for forwards is inadequate. I'm tempted to use the FRA-type notation next year because, in this situation, for example, f(0,1,3) would refer to the 2-year forward rate at the end of next year; i.e., today is time 0, the 2 year rate (3-1) starting in 1 year.

If i look at the source (see page 39 of the technical doc; thank you for this!), I agree with your statement: "could Saunders be talking about the *forward* rates f(1,2), f(1,3), f(1,4), f(1,5) [which would be the *spot* rates 1 year from now]?" The PV exercise in Saunders (p 337) and L. Allen (4.11, 4.13) is a spot-rate based PV but conducted one year forward. As evidenced by: it's four year cash flow on a five year bond.

As such, I don't think it compares *directly* to anything on Market B; it mixes forward and spot. It likely could be expanded to be only forward rates (e.g., the 4.32% that is the *future* 2-year spot could be broken into forward rates), then it would be a "pure" forward rate exercise.

Thanks for the discussion on this, kudos for going beyond the assignments

....David

append: I notice that CreditMetrics refers to this as "the one-year forward zero curve;" i.e., the spot rate curve in one year. Consistent with your take. I'd love to be corrected, but this is making me think (realize?) that proper forward notion really needs three numbers: time of pricing the rate (t0 typically), start of period, and term/end of period. I mean, typical is: as you have, f(1,2) which implies the one-year forward in one year. However, it implies we are estimating that forward rate today, this forward rate will change in six months, so i sort of wonder if a comprehensive notion would be f(0,1,2). Then a spot rate is f(0,0,1). Hmmm...