Forums  > Risk Management  > Does there exist a so called roll Greek (not theta!)?  
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Total Posts: 3604
Joined: Jun 2004
Posted: 2017-09-21 12:34
As far as I know the theta Greek/report
is calculated as keeping the today's market data
and repricing the deals, say, a day later. Makes perfect sense.

But I was told by an colleague about
the calculating the theta but moving the yield curve
as well. So basically shortening the deal by one day.
And he said that this thing is called roll and is wildly
used on bonds.

Could anyone share some light on this roll Greek/report?

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

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Total Posts: 1374
Joined: Mar 2004
Posted: 2017-09-21 17:29
I'm not a bond trader so will punt on that one, but in general thinking of theta in a model-dependent context makes sense.

Example: if I believe a particular local-vol model is great for a particular market then when moving forward in time my best guess of tomorrow's term vol may not be today's term vol, it could be the integral of the local vol model as seen with a day less (for same expiry). So then it's not crazy to take that into account when thinking about theta. Put differently, if your view of the dynamics is such that in the fully static case of your first paragraph, you expect that theta to be accompanied with a vega effect, then why not include that effect to get a "cleaner" theta? So people will produce different types of model dependent theta that way.

The bond case seems to be the same concept - depends on your view of how the yieldcurve behaves.

(It's probably *widely* used in bonds, not *wildly* Smiley)

Capital Structure Demolition LLC Radiation


Total Posts: 255
Joined: Dec 2010
Posted: 2017-09-21 18:27
You may be referring to the pnl impact in going from close -> open.

In general, yes, pnl predict, explain and unexplain are a big deal, especially on the buy-side, although not to be neglected on the buy side.

It's all about applying Taylor's theorem correctly, making some assumption on curve construction as a by-product.

There is something about that in Andreassen&Piterbarg, volume 3, under risk management, waterfall pnl, etc...

Rolling the book means, after closing the book on a given day (meaning snapping curves, vols, correlation, parameters, ...), you then roll the book to the next morning, so that you have a starting point when you get in next day.


Total Posts: 474
Joined: Jan 2015
Posted: 2017-09-21 19:07
Roll and theta are the same concept. They just differ by how you define "prices stay the same".

Say you're looking at monthly Eurodollar futures. So you have a 1 month contract expiring in October, a 2 month in November, etc. For simplicity let's also consider monthly theta, instead of daily. What does it mean in this context for prices to stay the same? One interpretation is that the October contract ends up at the same price as the October contract, the November->November, December->December, etc. Another way of viewing this is that next month's 1-month contract should end at the same price as today's 1-month. In which case the price of the October contract ends up at today's September price, November->October, December->November, etc.

Now if you extend it to daily, you might have 25-day contract today, which becomes a 24-day tomorrow. A 55-day that becomes a 54, etc. You don't have exactly the same expiry set day-to-day. So you interpolate between fixed point. A 55-day contract is 5/6 weight on the canonical 2-month contract and 1/6 weight on the 1-month. But in one day it will become more weighted to the 1-month. So, even if the curve doesn't move, this individual contract should slightly change prices to reflect it's change in weight. Like a wheel, where 1-full rotation is each monthly expiration, the contract "rolls" down a theoretically stable curve.

In fixed income, sometimes it's more natural to think about things in terms of their maturity, rather than specific securities. We care about "10-year treasury" yield and risk, not specifically CUSIP bond 9128282R0. If we wanted to compare our portfolio from 2 years ago to today, we wouldn't directly benchmark against CUSIP 9128282R0. We'd try to find two respective securities from each time period, that best correspond to "10-year treasury".

Good questions outrank easy answers. -Paul Samuelson


Total Posts: 2870
Joined: Feb 2005
Posted: 2017-09-22 08:37
It's probably *widely* used in bonds, not *wildly*

I think wildly is correct. Quants are a wild bunch at times Wink.

"He's man, he's a kid / Wanna bang with you / Headbanging man" (Grave Digger, Headbanging Man)


Total Posts: 3604
Joined: Jun 2004
Posted: 2017-09-22 08:54
Basically roll has sense.
Thank you very much, gentlemen.

> I think wildly is correct.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken


Total Posts: 1440
Joined: Jun 2004
Posted: 2017-10-29 21:13
Sometimes it is considered useful to separate the idea of roll down from theta

Rolldown captures the effect of your calibration instruments shortening in maturity by one day as you go from T to T+1. It is a predictable effect whose magnitude depends on the slope of the curve. Rolldown can be further split by curve roll and vol roll but this is probably excessive for most purposes.

Whereas pure theta incorporates the effect of optionality reducing by one day. So you would expect this to be zero for swaps and vanilla bonds.

As to how commonly this refinement is done, I'm not sure... I guess many people are happy with delta/vega plus "noise" attribution.
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