Why Floating-Rate Loans Return to Par on Reset Dates

Summary

The document gives a concise explanation for why a floating-rate loan is generally valued near par on a coupon reset date. At that date, the loan’s coupon is reset to the prevailing market rate. In the basic bond-pricing argument, an instrument whose coupon matches the market yield is priced at par, since its remaining cash flows are discounted at a rate consistent with that coupon. The proposed mathematical demonstration is to price the loan on the reset date after substituting the current market rate for the coupon rate.

This is a sketch rather than a full derivation. It does not specify payment timing, discount factors, credit spreads, fees, embedded options, or the details of how the floating benchmark and loan margin relate to the market rate. Those assumptions matter: a floating-rate loan may differ from par if its credit risk or required spread has changed, or if accrued interest and payment conventions are handled differently. The par result is therefore a useful reset-date intuition under standard simplifying assumptions, not a universal guarantee for every loan.

Key ideas

• A floating coupon resets to a reference market rate on reset dates.
• A bond with a coupon aligned to its market yield is priced at par in the basic valuation setup.
• The reset-date argument can be expressed by pricing cash flows with the coupon set to the current market rate.
• Credit spreads, loan terms, and payment conventions can cause actual loan value to depart from par.

Tags

# Floating Loan Valuation and Par Value


# Floating Loan Valuation and Par Value












Why is it true that the value of a floating rate loan is equal to its par value at payment dates?

How can one show this mathematically? I want to understand this both conceptually and mathematically.

## Answer by gaurav (score 1, accepted)

https://quant.stackexchange.com/a/49531

On every reset date, coupon rate is reset to current market rate & as we know that bond trades at par when coupon and market rates are same.

Mathematically, we just need to substitute coupon rate with market rate to price a bond on the reset date.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.