I am working on hedging agency MBSs using treasury bonds. So my question raise as which treasury bond should more likely be a hedging underlying of a MBS. What is the matching criteria usually for MBS hedging? Duration matching, coupon matching, maturity matching, or others.

Any MBS hedging opinions comments are welcome! I am using optimal monte carlo to do the hedge, so I need a more related hedging instrument.

  • 2
    $\begingroup$ What do you mean by optimal monte carlo? Duration matching is usually the standard. I know some also use swaptions to match the increase in the swap yields (which is linked to prepayment speed) $\endgroup$
    – adam
    May 5, 2014 at 6:37
  • $\begingroup$ @adam Great! Thanks adam! Someone alive! Optimal monte carlo basically is an optimization process for each time step in MC, usually taking the advantage of known final payoff and walk backwards, but here focuses on the hedging wealth change distribution at each time step, by minimizing the hedging wealth volatility, and constrain on wealth change expectation, using numerical approximation to solve option value and walk through, in the end based on the entire wealth change distribution to make better decision of pricing. I am still working on it, and apologize for my bad explanation. $\endgroup$
    – TomHan
    May 5, 2014 at 11:39

3 Answers 3


I would definitely not say CTD. And it's not even clear if it should be a UST.

In the past, MBS was hedged with USTs, but then MBS spreads blew out, and everyone realised that USTs could rally and MBS need not do the same. Or MBS could sell off like mad (spread widening) and the USTs might not do a thing. Basically, there has been blood spilled with every major lesson.

MBS is a spread product, so best to hedge with another spread product. So instead, people started using swaps. I could tell you more about how swaps are also a bad hedge, but anyhow....

Most MBS models give you a way for converting from PV to OAS and back again given a specific interest rate model. IR models take as an input swap curves (usually the 1m, 3m, 6m LIBOR swaps and Fed Funds for discounting) and vols. Really, you typically need all this stuff. To hedge, usually, you think of change in PV (keeping OAS fixed) for a given reshaping of the initial swap curve. Basically, the quants will have a way to bump each input swap, so the 2y swap, the 5y, the 7y, the 10y. You will get a delta to each swap.

So, any MBS exposure (even a single bond) will have deltas to each input swap. You'd never hedge them individually, but might if you had a large book.

Intuitively, if you just wanted to hedge with one underlying, it shifts about. The primary rate exposure for MBS is the Commitment rate (FN and FH both publish 30, 60 day commitment rates). The commitment rate is at times related to 10y swaps, at times much shorter, depending on the overall duration of outstanding MBS. It's a bit circular, but in a refi wave, you get a dependence which is closer to the 7y or shorter, and during a sell-off closer to 10y. Other people will model the commitment rate as related to some points on the swap curve with a vol component. I would say, if you really must hedge with one, look at the FH and FN commitment rates and figure out how their dependence on swaps of various durations has shifted through time.

  • $\begingroup$ Corrected USB - > UST. Sorry $\endgroup$
    – NBF
    Aug 6, 2018 at 14:22
  • $\begingroup$ This is a better answer imo $\endgroup$
    – Trajan
    Aug 6, 2018 at 14:29

MBS are of various types. Ones that are most rate sensitive are typically agency mortgages.

Rate Sensitivity

Rate sensitivity in mortgages comes from two parts:

  1. Its a stream of cashflow and like any other stream of cashflow (example treasury bond), it is sensitive to rates. This is referred to as duration of bond
  2. mortgages can prepay when prevailing rates in market are lower than the mortgage rate. This results in shortening of life of bond when rates in market reduces or extension of life when rates rise. This is referred to as gamma or convexity.


An approximate way to think about hedging is to short a treasury bond that has a tenor same as weighted average life (WAL) of mortgage bond. Why WAL? Because, mortgages are amortizing and weighted average cashflow life is smaller than their stated maturity. Typically, this is close to 7 year (i.e. typically an average life of mortgage is just 7 years as most likely it gets refinanced/prepay by then). Now, if mortgage has 7year WAL, this would mean that you can hedge using a 7yr treasury bond. However, 7yr treasury bond are not as liquidly traded. What hedgers end up using is therefore a mix of 5yr treasury bond and 10yr treasury bond in certain percentage so that weighted average duration is same as duration of 7yr bond (duration and WAL are not same but similar). You would however encounter situations where certain hedgers just use 10yr treasury bond to hedge (in an amount that is equal to duration of mortgage bond / duration of 10yr treasury).

More sophisticated way of hedging is to use all points on curve.. so hedge 2yr, 5yr, 10yr, 20yr and 30yr using mix of treasury bond so that overall duration ends up matching duration of mortgage bond


Cheapest to deliver treasury bonds as hedging underlying would be the most related instrument I can think of for your Monte-Carlo type. This leads to matching via conversion factors. I am basing my answer to the similarities of your method to Monte-Carlo tree search.

  • $\begingroup$ Great! @user7056 your answer is very practical, I think that is what used in real life, thanks! $\endgroup$
    – TomHan
    Jun 28, 2014 at 20:22
  • $\begingroup$ @TomHan i think the other answer is better $\endgroup$
    – Trajan
    Aug 23, 2018 at 18:17

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