Mixing SABR models for negative rates

Antonov, Konikov and Spector use an exact formula for the normal free boundary SABR to construct an arbitrage-free mixed SABR model

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Free stochastic alpha beta rho (SABR), an extension of the SABR model to negative rates, is not guaranteed to be arbitrage free. To resolve this, Alexandre Antonov, Michael Konikov and Michael Spector use an exact formula for the normal free SABR with arbitrary correlation to construct a mixed SABR model, a weighted sum of the normal and free zero-correlation models, that gives closed-form option prices. Added degrees of freedom allow joint to swaptions and constant m

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