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The Free Boundary SABR: Natural Extension to Negative Rates

In the current low-interest-rate environment, extending option models to negative rates has become an important issue. This white paper describes one such extension of the widely used SABR model. We stress that our solution is more natural and attractive than the shifted SABR. An exact formula is derived for the option prices in the case of zero correlation between the rate and its volatility. For nonzero correlation, a mapping procedure onto a mimicking zero-correlation model is applied. Analytical results for the suggested free-boundary SABR model are compared with Monte Carlo simulations.