We present two new stochastic volatility models in which option prices for European plain-vanilla options have closed-form expressions. The models are motivated by the well-known SABR model, but use modified dynamics of the underlying asset. The asset process is modelled as a product of functions of two independent stochastic processes: a Cox-Ingersoll-Ross process and a geometric Brownian motion. An application of the models to options written on foreign currencies is studied
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