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FRN Price/Yield Calculations

Floating rate notes are valued in exactly the same way as a standard fixed-coupon bond, i.e., discounting the future coupon payments from the FRN back to the settlement date. There are however at least two complications associated with applying the generic bond price formula to an FRN, and both relate to the determination of the uncertain future coupon amounts:

  • Unknown Coupon Periods: The main feature of an FRN is that the coupon rate for each coupon payment period is determined with reference to the value of an index at the beginning of each period. At any given valuation date, it is unknown what these rates will be, hence they are required to be forecasted based on a specific set of assumptions.
  • Choice of Coupon Payment Dates: For vanilla fixed-coupon bonds, the market standard assumption is that each coupon period has an equal length, and this in part gives rise to a coupon amount that is also constant. The actual cashflows for FRN's are dependent on the length of the coupon period. This means that even if the coupon rate is constant, the coupon amounts will differ across the life of the note. Calculation of price and yield for FRN's can therefore be based on different assumptions regarding coupon payment dates.

 

To reinforce the last point, note that in general the coupon amount for the i'th coupon period of an FRN (per $100 face value), assuming that the rate reset frequency and the payment frequency are the same, is computed as:

Equation Template

 

ci = coupon amount for the i'th coupon period.
ri = index level (as a percentage) as at the observation date for the i'th reset.
mq = quoted margin (as a percentage) relative to the index level.
DIP = number of days in the period, based on the selected accrual method.
DIY = number of days in the year, based on the selected accrual method.

 

Quite clearly, the assumption regarding the treatment of coupon dates will potentially cause the calculated value of DIP to change across coupon periods. If the "actual" number of payment dates is used in the calculation, the resulting coupon period lengths will differ and this will give rise to different coupon payments even if the reference rate is assumed to be the same for all reset dates.

 

The price/yield calculations of FRN's can be based upon three sets of assumptions.

 

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