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. Here, Alexandre Antonov, Michael Konikov and Michael Spector extend the widely used SABR model to the free boundary SABR model that can handle negative rates. They derive an exact option pricing formula for the zero correlation case, and a suitable approximation for the general case. The analytical results are successfully compared with the Monte Carlo simulations
The authors present a natural generalisation of the SABR model to negative rates and we describe its properties. They derive an exact formula for the option price in the zero-correlation case and an efficient approximation for general correlation written in terms of a one-dimensional integral of elementary functions.
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