Cutting Edge introduction: SABR rattling

SABR rattling

mathematics

A basic rule of probabilities – leaving aside some esoteric, contrarian lines of thought in academic literature – is that they are positive numbers. But there is a curious defect in the standard way of generating volatility smiles for the stochastic alpha beta rho (SABR) model that is the industry benchmark for interest rate options – it can imply negative probabilities for the underlying to fall below very low strikes.

In the pre-crisis days of 5% Libor, this could be dismissed as an irrelevant

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