The step stochastic volatility model

Extreme short-dated skew can be obtained by decomposing it in two parts

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Peter Friz, Paolo Pigato and Jonathan Seibel propose a modification of a given stochastic volatility model ‘backbone’ capable of producing extreme short-dated implied skews, without adding jumps or non-Markovian ‘rough’ fractional volatility dynamics. A decomposition formula for the implied skew of a local stochastic volatility model suggests this can be achieved via a non-smooth leverage function, such as a step function. The resulting step stochastic volatility