The Randomised Heston Model

35 Pages Posted: 27 Aug 2016 Last revised: 6 Dec 2018

See all articles by Antoine (Jack) Jacquier

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Fangwei Shi

Imperial College London

Date Written: August 25, 2016


We propose a randomised version of the Heston model -- a widely used stochastic volatility model in mathematical finance -- assuming that the starting point of the variance process is a random variable. In such a system, we study the small- and large-time behaviours of the implied volatility, and show that the proposed randomisation generates a short-maturity smile much steeper ('with explosion') than in the standard Heston model, thereby palliating the deficiency of classical stochastic volatility models in short time. We precisely quantify the speed of explosion of the smile for short maturities in terms of the right tail of the initial distribution, and in particular show that an explosion rate of t^r (r in [0,1/2]) for the squared implied volatility -- as observed on market data -- can be obtained by a suitable choice of randomisation. The proofs are based on large deviations techniques and the theory of regular variations.

Keywords: Stochastic volatility, large deviations, Heston, implied volatility, asymptotic expansion

JEL Classification: C6, G13

Suggested Citation

Jacquier, Antoine and Shi, Fangwei, The Randomised Heston Model (August 25, 2016). Available at SSRN: or

Antoine Jacquier (Contact Author)

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom


The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Fangwei Shi

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

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