Replicating a European Swaption with a Forward-Starting Swap

Summary

The document clarifies what swap underlies a European payer swaption whose exercise date is in the future and whose swap tenor begins at that date. Its example has a five-year option maturity and a ten-year tenor. The key distinction is between the ten-year swap tenor and the swap’s changing forward start: at inception, the underlying is a ten-year swap starting five years ahead. As time passes before expiry, the start date moves closer while the underlying tenor remains ten years.

This gives a useful way to identify the evolving underlying exposure when thinking about a replication strategy. It does not, however, derive a replication portfolio, specify a hedge ratio, or explain how to fund or rebalance a hedge. The question asks whether a position in the swap plus a risk-free asset suffices, but the answer only corrects the description of the underlying. Accordingly, the note is conceptual rather than a complete pricing or hedging method; further assumptions about rates, market instruments, and the swaption’s valuation model would be needed to construct a replicating strategy.

Key ideas

• A European swaption’s underlying is a forward-starting swap that begins on the option exercise date.
• The underlying swap tenor stays fixed as time passes before expiry.
• The forward start shortens as the option approaches maturity.
• Identifying the underlying does not by itself specify a replicating portfolio or hedge ratio.

Tags

# Replication of European swaption


# Replication of European swaption












Suppose we have a European payer swaption with 5-year maturity and 10-year tenor. The underlying is clearly the 10-year tenor payer swap. Does it mean that to replicate the swaption I need to construct a self-financing portfolio that is long an amount $\Delta$ of the 10-year payer swap and short the risk-free asset?

## Answer by user42108 (score 1, accepted)

https://quant.stackexchange.com/a/58710

The underlying is clearly the 10-year tenor payer swap.

The underlying is - initially - the 10y swap, 5y forward. In a year from now, it will be the 10y swap, 4y forward (etc).

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