Why Interest Rate Swap Valuation Uses Curve-Implied Forward Rates

Summary

The document addresses why interest rate swaps are often valued using forward rates derived from today’s yield curve instead of simulating each future floating payment. It explains that spot rates are bootstrapped from traded instruments and imply forward rates through no-arbitrage relationships. If a forward rate diverged from the curve-implied rate, positions in traded maturities could replicate the forward exposure and create an arbitrage opportunity.

As an illustration, it describes replicating a future six-month rate using positions in one-year and six-month rates. This explains why current forward rates provide the market-consistent inputs for standard valuation. The document is brief and does not detail swap cash-flow discounting, simulation methods, or models for stochastic rates. Its explanation concerns arbitrage-consistent pricing inputs; it does not imply that future rates are known with certainty or that simulation has no role in risk analysis or more advanced models.

Key ideas

• Forward rates are implied by spot rates bootstrapped from traded instruments.
• No-arbitrage arguments constrain forward rates to match those implied by the yield curve.
• A future six-month rate can be replicated using positions in longer and shorter rate exposures.
• Curve-implied forwards support standard swap valuation, while the document does not cover stochastic-rate simulation in depth.

Tags

# Why are Interest Rate Swaps not valued using Monte Carlo Simulations?


# Why are Interest Rate Swaps not valued using Monte Carlo Simulations?












the current valuation methods seem to rely on treating the floating payment as deterministic based on the current yield curve and derived forward rates. But wouldnt it make more sense to use monte carlo simulation or other methods to account for the random nature of interest rates and the fact that we will not know future floating cash flows?

## Answer by David Duarte (score 8, accepted)

https://quant.stackexchange.com/a/51266

Forward rates are determined from current spot rates bootstrapped from traded instruments. The reason is that if the forwards were different from the ones inferred from the spot rates, there would be arbitrage.

For example, you can replicate a forward 6 month rate in 6 months with a long position in the one years rate and a short position in the 6 month rate.

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.