Swaptions: 1 Price, 10 Deltas, and… 6 1/2 Gammas*: Wilmott Magazine Article
In practice, option pricing models are calibrated using market prices of liquid instruments. Consequently for these instruments, all the models give the same price. But the risk implied by them can be widely different. This note compares simple risk measures (first and second order sensitivity to the underlying yield curve) for simple instruments (swaptions). The main conclusion is that the hedging varies widely (up to 10% of the underlying risk) between the models, with the prevailing differentiating factor being the model dynamic.
The shape of the smile has also an impact but to a lesser extent. Hedging efficiency using historical simulation is analysed. Using data from the last three years, normal-like models perform consistently better.
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