Thursday, December 12, 2013

family photo ^ family video - yield curve

snapshot - The yield curve (yc) is a snapshot.
snapshot - term structure of IR is another name of the yc.
snapshot - discount curve is the same thing

On a given snapshot, we see today's market prices, yields and rates of various tenors[1]. From this snapshot, we can derive[2] a forward discount factor between any 2 dates. Likewise, we can derive the forward 3M-Libor rate for any target date.

Looking at the formula connecting the various rates, it's easy to mix the family photo vs the family video.
- family photo is the snapshot
- family video shows the evolution of all major rates (about 10-20) on the family photo.
** an individual video shows the evolution of a particular rate, say the 3M rate. Not a particular bond, since a given bond's maturity will shrink from 3M to 2M29D in the video.

All the rate relationships are defined on a snapshot, not on a video.

I guess we should never differentiate wrt to "t", though we do, in a very different context (Black), integrate wrt "t", the moving variable in the video.

An example of a confusing formula is the forward rate formula. It has "t" all over the place but "t" is really held as a constant. The t in the formula means "on a given family photo dated t". When studying fixed income (and derivatives) we will encounter many such formula. The photo/video is part of the lingo, so learn it well.

Also, Jeff's HJM slide P12 shows how the discount bond's price observed at time t is derived by integrating the inst fwd rates over each day (or each second) on a family photo.

[1] in an idealized, fitted yc, we get a yield for every real-valued tenor between 0 and 30, but in reality, we mostly watch 10 to 20 major tenors.

[2] The derivation is arbitrage free and consistent in a risk-neutral sense.

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