Mastering Attribution in Finance

APPENDIX B

Explicit pricing of an FRN

The price P of an FRN per $100 face value is given by the expression

where

• R_T is the reference rate at the last coupon reset date T;
• M is the reset margin;
• DM is the discount margin;
• r is the zero rate at the next coupon payment date;
• d is the number of days in the current interest period;
• f is the number of days from settlement date to next coupon date;
• a_n = (1 − vⁿ)/i;
• v = 1/(1 + i);
• i = (S + DM)/n;
• S is the annual swap rate from settlement to maturity of the FRN;
• n is the number of interest periods to maturity at the next coupon date.

Quarterly coupons and a 365-day year are assumed.

The expression ...