Trading a Violation of a Swaption Price Inequality

Summary

The document asks how to trade a violation of a stated no-arbitrage inequality involving three swaptions with the same strike and different option and swap maturities. The condition says the prices of two shorter-maturity swaptions, taken together, should be at least as large as the price of the longer-maturity swaption.

The proposed trade is to sell the two swaptions on the left side and buy the one on the right. If the inequality is violated, this direction sells the more expensive combination and buys the cheaper instrument, generating an apparent price discrepancy. The response makes clear that identifying and observing such a violation is the difficult part; it does not explain how to source reliable market prices or execute the positions. It also provides no discussion of contract matching, transaction costs, liquidity, or other practical risks that could affect an arbitrage trade.

Key ideas

• The stated no-arbitrage condition compares a pair of swaptions with a single longer-maturity swaption.
• If the condition is violated, the suggested position sells the pair and buys the single swaption.
• The trade aims to sell the more expensive side and buy the cheaper side.
• The response does not address execution costs, liquidity, or how to detect a reliable violation.

Tags

# Swaption Volatility Cube arbitrage


# Swaption Volatility Cube arbitrage












How can I exploit an arbitrage by violating the following no-arbitrage condition (taken from the paper "Arbitrage-Free Construction of the Swaption Cube" by Simon Johnson and Bereshad Nonas):

Swptn(K,T1,T2)+Swptn(K,T2,T3) >= Swptn(K,T1,T3) with Swptn(A,B,C) being the price of a swaption of strike A, time to option maturity B, time to underlying swap maturity C.

Thanks for any hints. L.

## Answer by MFib (score 1)

https://quant.stackexchange.com/a/25265

Exploiting an arbitrage is straightforward. Constructing and noticing one is the hard part. In your case if you know that Swptn(K,T1,T2)+Swptn(K,T2,T3) >= Swptn(K,T1,T3),

Simply sell Swptn(K,T1,T2)+Swptn(K,T2,T3) and buy Swptn(K,T1,T3). Sell the most expensive and buy the cheapest.

L.

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