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It is the intention choose any equivalent martingale measure, so that the drift of volatility process, respect at the new measure, is zero. This technique is possible when the Girsanov theorem is satisfied, since the stochastic volatility models are uncompleted markets, thus one has to choice an arbitrary risk price of volatility. In all this cases the authors are able to compute the price of Vanilla options in a closed form. To name a few, they can think to the popular Heston's model, in which the solution is known in literature, unless of an inverse Fourier transform.
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