Given that which bond in the basket becomes CTD depends massively on idiosyncratic moves among different bonds, should we not be always using N factor model instead of 2 Factor model?

By using only 2 Factors we are only capturing Slope and Level changes but ignoring curvature and other higher order movements which should, in theory, be also very important for determining CTD, especially when we have lots of closely contending bonds.

By 2 Factor model, I mean modeling yields using first two factors only.

  • 2
    $\begingroup$ Could you shortly explain the two-factor model for bond futures that you mean here? $\endgroup$
    – Richi Wa
    Sep 16, 2014 at 15:48
  • $\begingroup$ @Richard. From his post it sounds like he is talking about using PCA on yield levels and taking the first 2 components to model how price would change for a given change in yield. $\endgroup$
    – meh
    Aug 4, 2015 at 20:43
  • $\begingroup$ Right ... with the edit of "first two" this is very likely. $\endgroup$
    – Richi Wa
    Aug 5, 2015 at 6:28

1 Answer 1


There's always a balance between model complexity and interpretability. Of course, it'll be great if we can perfectly capture the comovement of all the bonds in the deliverable basket, but that would require the volatilities of all the bond's yields and the correlations amongst all these bonds as well -- it's not easy to come up with reliable assumptions for these...

Two-factor models typically depend on PCA to capture the co-movements of bond yields. My personal experience is that this works well enough -- in most environments, the first two principle components would capture 85-99% of the variances already. As to the residual, instead of thinking about "changes in curvature," I'd rather focus on the relative richening/cheapening of individual bonds, either relative to a fitted bond curve or on asset swap basis. This can be easily incorporated into your model.

At the end of the day, these models are meant to help with trading decisions, and 2-factor models are very easy to "think through." Personally, when looking at basis, I'd either take the duration/curve risks or hedge them out. This can be done very easily within a 2-factor framework.

Finally, there are so many intricacies involved when modeling bond futures/basis:

  1. Are you using the correct implied volatility?
  2. How do you model bonds that haven't even been auctioned yet? How rich should these issues be trading relative to current on-the-runs?
  3. Will the CTD and near-CTDs trade special in the repo market?
  4. Is the fed active and thus will repo rates increase/decrease substantially?

All of these factors can easily dominate the 3rd or 4th PCA factors...

P.S. I'm assuming you're not using one of those 2-factor short-rate models, right? Those don't work very well..

  • $\begingroup$ nice said. just curious, if not short-rate models, which ones are you using? LMM? $\endgroup$
    – athos
    Sep 19, 2014 at 3:10
  • $\begingroup$ @athos i do know people who use LMM. I haven't tried that personally; I diffuse bond yields directly. $\endgroup$
    – Helin
    Sep 19, 2014 at 16:35
  • $\begingroup$ Directly? I thought there shall always be something like LMM or HJM behind it. Mind to elaborate a bit ? $\endgroup$
    – athos
    Sep 19, 2014 at 22:26
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    $\begingroup$ @athos It's actually embarrassingly simple... Let's say you have a bond whose yield is x% today (this is its yield to maturity, not a short rate). Then at the next time step, based on today's yield & the yield volatility, you can get its new yields in different states. You just need to make sure the expected price on this date matches the bond's forward price to maintain no-arbitrage. You can either use a tree/grid or run a Monte Carlo. $\endgroup$
    – Helin
    Sep 21, 2014 at 0:02
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    $\begingroup$ @athos not exactly. Strictly speaking, you don't even need the full yield curve. You already have every deliverable's yield as of today. Given their repo rates (also known), it's straightforward to compute their forward prices. And PCA gives you the relative yield movements of these deliverables. That's pretty much all the ingredients you need. $\endgroup$
    – Helin
    Sep 21, 2014 at 2:04

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