SABR goes normal

The benchmark stochastic alpha beta rho model for interest rate derivatives was designed for an environment of 5% base rates, but its traditional implementation method based on a lognormal volatility expansion breaks down in today’s low-rate and high-volatility environment, returning nonsensical negative probabilities and arbitrage. Philippe Balland and Quan Tran present a new method based on a normal volatility expansion with absorption at zero, which calibrates while eliminating arbitrage in the lower strike wing

falling rates

The stochastic alpha beta rho (SABR) model is the industry standard for interest rate derivatives. However, it was designed at a time when most curves were at much higher levels than today’s ultra-low-rate environment. Problems with its implementation, through the so-called Hagan expansion, such as the breakdown of the expansion for high volatility and the possibility of negative probabilities for very low strikes, did not matter at the time but now constitute a pressing problem for the swaps

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