A stochastic volatility alternative to SABR. (English) Zbl 1152.91683

Summary: 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.


91B70 Stochastic models in economics
60K99 Special processes
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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