Replicating a Forward-Starting Swap with Spot-Starting Swaps

Summary

The document describes how to approximate a forward-starting interest rate swap using ordinary spot-starting swaps. For a forward swap beginning after an initial period, one can receive a longer-tenor swap and pay a shorter-tenor swap with matching notionals and fixed rates. The overlapping early cash flows offset, leaving the later-period exposure of the forward swap.

This is presented as a static cash-flow replication, so the positions do not require dynamic rebalancing to preserve that offset. In practice, the market may only offer the component swaps at current market rates rather than at the desired forward rate. That difference leaves residual cash flows, which may need additional hedging with other swaps. A second response gives a shorter-tenor example and cautions that the approximation works better for shorter forward starts. The document does not provide valuation formulas, sensitivity calculations, or a numerical measure of replication error, so it offers a trading construction rather than a complete pricing treatment.

Key ideas

• A forward-starting swap can be replicated by combining a longer swap with an offsetting shorter swap.
• Matching notionals and rates causes the overlapping early cash flows to cancel.
• The remaining cash flows represent the later forward period.
• Market-rate differences from the target forward rate can leave residual exposure to hedge.
• The proposed approximation is reported to work better for shorter forward starts.

Tags

# Forward swap sensitivity


# Forward swap sensitivity












How do we replicate a forward swap using ordinary swap? Do we have either sensitivity or present value on forward interest rate swap prior to the effective date?

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/51234

Say you received on a 5y5y swap at 2% in 100m notional.

You could directly simulate this via receiving a 10y swap at 2% in 100m and paying a 5y swap at 2% in 100m.

The first 5y worth of cashflows will fully net out leaving the residual swap. This is a permanent replication, i.e. once you have executed all trades there is no need for dynamic hedging at different market levels to maintain the cashflow neutrality.

However, in practice the market might only permit you to replicate with 10y and 5y swaps at market rates (i.e. other than 2% on the forward), which generally creates some residual cashflows that will also need hedging with other swaps, but those are quite small comparatively.

## Answer by Edward Watson (score 0)

https://quant.stackexchange.com/a/51233

It’s not a perfect replication and works better for shorter forward starts but receiving 1x 2 year and paying 1x 1 year is close to a 1 year forward 1 year.

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.