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For the past two decades, local stochastic volatility (LSV) models have been enjoying a great deal of popularity among practitioners, not only as term structure models for the pricing and risk management of complex products (see, for example, Andersen & Piterbarg 2010; Blacher 2001; Lipton 2002), but also for the modelling of vanilla options (see, for example, Berestycki et al (2004) and the widely used
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