The textbook example assumes that discount curve and projection curve are the same (or have a perfect correlation). What happens with the FRN's duration when it is not the case?

For example, there are bonds with floating coupons every 6M, but the index for their coupon rate is linked to the 5Y point on the government bonds curve. Every 6M they pay the yield of 5Y government bond + spread.

How could we find the duration of such a bond (disregard the spread for clarity)?

  • $\begingroup$ Taking a step back, what are you trying to achieve? Are you trying to quantify the sensitivity of the instrument to interest rates and their implied vols? Is someone forcing/mandating you to calculate durations? Would the dollar impact of a small change in interest rate change by tenor bucket, and vega, be easier to understand than (key rate) duration? $\endgroup$ Commented Feb 6 at 12:37

1 Answer 1


In that case the duration needs to be carefully defined and interpreted. To first order, the duration is approximately zero, because the simplest assumption is to move the projection curve (5yr Treasury forward rates) and discount curve in parallel. But this is obscuring key information : holding such a FRN amounts to having a curve steepening trade - you win if the 5yr projected rates go up more than the 6month forward rates. This can be more precisely measured by computing the partial durations by shocking different parts of the curve.

  • $\begingroup$ Just thinking out loud - if a model prices such a bond, or explains its observable price - then we project 5Y rate for future unset coupons probably using convexity adjustment probably using implied vol - so one should calculate and monitor the vega. Suggested paper for OP: papers.ssrn.com/sol3/papers.cfm?abstract_id=3401235 Also, given the bet on the shape of the interest rate curve, reporting sensitivities to historical principal components of the curve might be even more informative than to individual tenors. $\endgroup$ Commented Feb 7 at 13:52
  • $\begingroup$ If you traded this type FRN and traded a CMS (vs 5Y) and traded an IRS, would you not synthesise a traditional FRN? In which case is its pricing and risk sensitivities determined by the combination of a regular FRN, CMS and IRS? $\endgroup$
    – Attack68
    Commented Feb 8 at 17:12

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