The Step Stochastic Volatility Model (SSVM)

Abstract

Stochastic Volatility Models (SVMs) are ubiquitous in quantitative finance. But is there a Markovian SVM capable of producing extreme (T^(-1/2)) short-dated implied volatility skew?

We here propose a modification of a given SVM "backbone", Heston for instance, to achieve just this - without adding jumps or non-Markovian "rough" fractional volatility dynamics. This is achieved via non-smooth leverage function, such as a step function. The resulting Step Stochastic Volatility Model (SSVM) is thus a parametric example of local stochastic volatility model (LSVM). From an IT perspective, SSVM amounts to trivial modifications in the code of existing SVM implementations. From a QF perspective, SSVM offers new flexibility in smile modelling and towards assessing model risk. For comparison, we then exhibit the market-induced leverage function for LSVM, calibrated with the particle method.

Keywords: local stochastic volatility, implied volatility, implied skew, particle method

JEL Classification: G12, G13