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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?

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2 Answers 2

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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.

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  • $\begingroup$ Yeah but the cash flows still won’t match because the off market swaps will require payments or credits on either a cash debit or credit right? $\endgroup$ Feb 18, 2020 at 19:31
  • $\begingroup$ at 2%, 2% and 2% all of the contractual cashflows will be fully replicated and net. The collateral (due to off market swaps) will also be identical (upon netting) since the replicated cashflows must have the same overall value, presumably zero at initiation. In the case of using market rates, i.e. 2% x% and y%, then there will be a non-replicable cash flow profile that needs additional hedging, although as stated this is generally much smaller comparably $\endgroup$
    – Attack68
    Feb 18, 2020 at 19:37
  • $\begingroup$ I agree. Here's a little simplified proof i did: duration 1.75 4.25 term 2.00 5.00 rate 1.00% 2.00% fwd 2.67% fwd-spot 1.67% 0.67% pv 2.926 2.857 $\endgroup$ Feb 18, 2020 at 19:52
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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.

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