Extending SABR Model to Negative Rates
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In the low or negative interest rates environment, extending option models to negative rates becomes important. This chapter describes two such extensions of the SABR model: free SABR and mixture SABR. For free SABR, an exact formula is derived for 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. Mixture SABR always has a closed-form solution for option prices, and has additional degrees of freedom allowing it to calibrate to a broader set of trades, e.g a set of swaptions and a CMS payment. Analytical results for free and mixture SABR models are compared with the Monte Carlo simulation ones.