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Managing Smile risk from Hagan et. al. Generally if you pre-select $\beta$, it is from a priori considerations. $\beta = 1$ corresponds to stochastic lognormal $\beta = 0$ is stochastic normal $\beta=1/2$ CIR In the SABR model, beta is usually calibrated first, followed by the other 3 parameters. Frequently, instead of calibrating beta, it is simply ...


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