Markovian Projection Onto a Heston Model

31 Pages Posted: 28 Jun 2007

Date Written: June 27, 2007

Abstract

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: https://ssrn.com/abstract=997001 or http://dx.doi.org/10.2139/ssrn.997001

Alexandre Antonov (Contact Author)

Danske Bank - Danske Markets ( email )

Holmens Kanal 2-12
DK-1092 Copenhagen K
Denmark

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

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