snapshot - The yield curve (yc) is a snapshot.

snapshot - term structure of IR is another name of the yc.

snapshot - term structure of IR is another name of the yc.

snapshot - discount curve is the same thing

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.

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.

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

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