Gamma Exposure in Floating-for-Floating Basis Swaps

Summary

The document considers whether a same-currency floating-for-floating interest rate swap has gamma, meaning sensitivity of value to changes in rates. It contrasts two views: distinct indices with different yield curves can create gamma, while a typical tenor basis swap may have negligible gamma in practice.

The practical explanation is that a move in the basis spread changes the swap’s value in a way that can be represented as a fixed annuity whose present value depends on outright interest rates. Correlation between outright rates and basis spreads can therefore make the exposure resemble gamma, but the answer describes this as uncommon based on experience. The discussion is brief and gives no derivation, market data, or quantitative measure, so the conclusion should be treated as a qualitative rule of thumb rather than a general result for every structure.

Key ideas

• Different floating indices can have different yield curves, giving a basis swap potential rate convexity exposure.
• A typical tenor basis swap is described as having negligible gamma in practice.
• Basis movements create value changes through an annuity whose present value depends on outright rates.
• Correlation between outright rates and basis spreads can produce gamma-like effects.

Tags

# Is there any gamma in basis (i.e., floating for floating) interest rates swaps?


# Is there any gamma in basis (i.e., floating for floating) interest rates swaps?












It is well known that vanilla fixed for floating swaps usually have a bit of gamma, but does a floating for floating (basis) swap have any? For the sake of simplicity, let's assume that both legs of the swaps are in the same currency.

## Answer by Akshay (score 1)

https://quant.stackexchange.com/a/1718

Yes, if the two rates belong to two different currencies having different yield curves. Or in fact any two indices (bases) having different yield curves. e.g OIS vs LIBOR or LIBOR vs UST etc.

## Answer by dm63 (score 0)

https://quant.stackexchange.com/a/24907

In practice a 3s-1s basis swap has negligible gamma. Imagine putting on the basis swap, then the basis swap market moves. The resulting profit or loss is the present value of a fixed annuity, whose value depends on outright rates, not basis swaps. Sometimes there could be a correlation between rates and basis swaps, which could make this covariance feel like a gamma position, but this is relatively rare in my experience.

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