Floating-Leg Swap Valuation: Forward Rates and Discounting

Summary

The document compares two approaches to valuing an interest rate swap’s floating leg. A traditional shortcut treats the leg as a par bond worth its notional immediately after a floating payment, while accounting separately for the first known coupon. This shortcut embeds an assumption that the discount curve is flat at the reference floating rate, such as LIBOR.

The alternative projects future floating coupons using forward rates and discounts those cash flows using the applicable discount curve. The accepted explanation says this better reflects modern collateralized valuation conventions, which commonly use an overnight rate such as Fed Funds or EONIA for discounting. The distinction matters when projection and discounting curves differ. The document gives a concise conceptual explanation, but no worked example, market data, or detailed treatment of curve construction, payment timing, or collateral terms; those conventions must be specified in an actual valuation.

Key ideas

• The par-bond shortcut for a floating leg assumes discounting at the floating reference rate.
• Forward rates can be used to project future floating payments.
• Projected cash flows should be discounted using the applicable discount curve.
• Separate projection and discount curves can change swap valuation.

Tags

# Swap Pricing - Using forward rates vs using par bond after first floating payment


# Swap Pricing - Using forward rates vs using par bond after first floating payment












There seems to be two different methods I have come across for valuing a Interest Rate Swap - specifically the floating leg.

One method described by Hull: incorporates the cashflow from the first known floating leg payment, then immediately after this adds in 100 to the cashflow - To represent a fairly priced bond.

Another method actually uses the forward rate as the expectation of what the swap rate will be.

Opinions/explanations on these methods?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/46514

The first method assumes that the value of a floating leg at libor flat is 100. This contains an inbuilt assumption that the discount rate is Libor flat, which is an assumption that used to be made. Nowadays , we discount cash flows at Fed Funds (or Eonia in Europe), so the second method is better: first replace the floating rates by their forward rates, then discount at Fed Funds.

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