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FRN - Equal Coupon Rates & Exact Coupon Periods

While the coupon rate for each rate reset period is still assumed to be equal under this assumption, the coupon payments now depend on the length of the coupon period. This means that the valuation formula must now consider each of the future coupons separately. As such, the dirty price of an FRN is calculated as:

Equation Template

P = dirty price (clean price plus accrued interest) of the FRN per 100 units face value.

c1 = the first/next coupon payment. For an odd first period, this amount may differ from the standard coupon payment. It may also equal zero if the bond is trading ex-coupon.

c2 = the coupon payment due on the next nominal payment date. For bonds with an odd first period, this amount may differ from the standard coupon payment.

c = the i'th coupon payment per 100 units of face value, based on the constant coupon rate and the assumption that normal coupon periods have exact length.

cfn = the final coupon amount for a bond with an odd final period. This is zero for all other bonds.

n = the number of standard coupon periods between the coupon payment date and the maturity date. If the bond has a long last coupon period, then n does not include the normal quasi coupon period at the beginning of the long last period.

v = the discount factor for a standard coupon period, again based on the assumption of coupon periods with exact length.

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.

ym = the required annual nominal yield to maturity, expressed as a decimal. With a given price for the FRN, this is the initial yield parameter that is solved for (see calculation of effective margin).

 

 

For FRN's that do not have odd first or last periods, we can further define some of the inputs into the above equation as follows:

Equation Template

d1 = the number of days between the settlement date and the first coupon payment date.

h = the number of coupon periods in a year.

r1 = the reference index rate observed at the beginning of the current coupon period.

rf = the forecast reference index rate for all future coupon periods.

 

If the FRN has either an odd first or last period, then the coupon amounts are defined as follows:

 

 

 

c1

 

c2

 

..

Short First Period

Equation Template

Equation Template

Long First Period

 

0

Equation Template

 

 

 

 

 

cfn

 

 

..

 

Short Last Period

Equation Template

 

Long Last Period

Equation Template

 

 

 

 

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