Markovian Projection Onto a Heston Model

31 Pages Posted: 28 Jun 2007

See all articles by Alexandre Antonov

Alexandre Antonov

Abu Dhabi Investment Authority; ADIA

Timur Misirpashaev

Bloomberg LP

Vladimir Piterbarg

NatWest Markets; Imperial College London

Date Written: June 27, 2007


We develop a systematic approach to the reduction of dimensionality of smile-enabled models by projecting them onto a displaced version of the two-dimensional Heston process. The projection is the key for deriving efficient, analytical approximations to European option prices in such models. This is a further development of the method of Markovian projection previously used for projecting on the displaced-diffusion process (with skew but without smile). The method is derived in a generic form and has a wide range of suitable applications. Examples for spread and basket options are given.

Keywords: Markovian projection, stochastic volatility, Shifted Heston model, Gyongy lemma, index options, Heston basket options, Heston spread options

JEL Classification: C1,C3,C5,C6

Suggested Citation

Antonov, Alexandre and Misirpashaev, Timur and Piterbarg, Vladimir, Markovian Projection Onto a Heston Model (June 27, 2007). Available at SSRN: or

Alexandre Antonov (Contact Author)

Abu Dhabi Investment Authority ( email )

211 Corniche Road
Abu Dhabi, Abu Dhabi PO Box3600
United Arab Emirates

ADIA ( email )

211 Corniche
abu Dhabi
United Arab Emirates

Timur Misirpashaev

Bloomberg LP ( email )

731 Lexington Ave
New York, NY 10022
United States

Vladimir Piterbarg

NatWest Markets ( email )

250 Bishopsgate
London, EC2M 4AA
United Kingdom

Imperial College London ( email )

South Kensington Campus
Imperial College
United Kingdom

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