Hedging Long-Dated Swap Convexity with Short-Dated Swaptions

Summary

The document proposes a way to hedge the convexity of long-dated fixed cash flows, using a long-maturity swap as the example. The theoretical construction is to sell at-the-money payer and receiver swaptions with very short expiries, sized according to the swap’s calculated convexity. Their underlying swap maturity would move forward alongside the long-dated position, a structure described as a mortgage replication trade.

For practical implementation, the response suggests using options with expiries such as one, three, or six months rather than one-day options. It also says that keeping the underlying maturity moving may matter less in practice. The proposal is brief and does not show sizing calculations, risk sensitivities, market assumptions, or performance evidence. It therefore outlines a possible hedge structure, not a full implementation guide; users would need to assess residual risks and the suitability of the option terms for their cash flows.

Key ideas

• A long-dated swap's convexity can theoretically be hedged with short-expiry at-the-money payer and receiver swaptions.
• The proposed option amounts are tied to the calculated convexity of the swap.
• The underlying swap maturity can be made to move forward with the long-dated position.
• The response suggests using one-, three-, or six-month options in practice and identifies the approach as mortgage replication.

Tags

# Hedging convexity for long-dated fixed cashflows


# Hedging convexity for long-dated fixed cashflows












I'm wondering what are the different ways of hedging the convexity in fixed long-dated cashflows (maturity > last liquid point). Also, if you'd say receiver swaptions would be the way to go, could you elaborate a bit on why this is the case? Thanks a lot and quant away! :)

## Answer by Edward Watson (score 1)

https://quant.stackexchange.com/a/47234

I think theoretically if you were trying to hedge the convexity of a 30yr swap you could sell 1 day atm receiver and payer swaptions where the underlying is also maturing ("walking") along with your 30yr swap, in the amount of the calculated convexity of the 30yr swap on that day. In practice you would do 1m,3m or 6m type options and maybe have the underlying walking but it doesn't matter that much. This is also more well known as a mortgage replication trade.

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