The Step Stochastic Volatility Model (SSVM)

20 Pages Posted: 4 Jun 2020

See all articles by Peter Friz

Peter Friz

Technische Universität Berlin (TU Berlin)

Paolo Pigato

University of Rome Tor Vergata - Department of Economics and Finance

Jonathan Seibel

Munich Re

Date Written: May 7, 2020

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

Suggested Citation

Friz, Peter and Pigato, Paolo and Seibel, Jonathan, The Step Stochastic Volatility Model (SSVM) (May 7, 2020). Available at SSRN: https://ssrn.com/abstract=3595408 or http://dx.doi.org/10.2139/ssrn.3595408

Peter Friz

Technische Universität Berlin (TU Berlin) ( email )

Straße des 17
Juni 135
Berlin, 10623
Germany

Paolo Pigato (Contact Author)

University of Rome Tor Vergata - Department of Economics and Finance

Via Columbia 2
Rome, Rome 00123
Italy

Jonathan Seibel

Munich Re ( email )

Königinstr. 107
Munich, 80802
Germany

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