Markovian Projection to a Displaced Volatility Heston Model

20 Pages Posted: 20 Mar 2008

See all articles by Alexandre Antonov

Alexandre Antonov

Abu Dhabi Investment Authority; ADIA

Matthieu Arneguy

Numerix

Nicolas Audet

Numerix - Quantitative Research

Date Written: March 12, 2008

Abstract

Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian Projection target, is an example.

In this article, we generalize the results of Markovian Projection onto a Heston model to a wider class of approximating models, a Heston model with displaced volatility. As an important application, we derive an effective approximation for FX/EQ options for the Heston model, coupled with correlated Gaussian interest rates.

The main technical result is an option evaluation for correlated Heston/Lognormal processes. Unlike the case of exactly solvable (affine) zero correlation or its uncorrelated displacement generalization,considered by Andreasen, non-trivial correlations destroy affine structure and exact solvability.

Using the powerful technique of Markovian Projection onto a Heston model with displaced volatility, we produce an effective approximation and present its numerical confirmation.

Keywords: Markovian projection, stochastic volatility, Heston model, Gyongy lemma, Heston/Hull-White correlated hybrid, FX-options approximation

JEL Classification: C1, C3, C5, C6

Suggested Citation

Antonov, Alexandre and Arneguy, Matthieu and Audet, Nicolas, Markovian Projection to a Displaced Volatility Heston Model (March 12, 2008). Available at SSRN: https://ssrn.com/abstract=1106223 or http://dx.doi.org/10.2139/ssrn.1106223

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

Matthieu Arneguy

Numerix ( email )

41 Eastcheap
London, EC3M 1DT
United Kingdom
+44(0)2076486100 (Phone)

HOME PAGE: http://www.numerix.com

Nicolas Audet

Numerix - Quantitative Research ( email )

41 Eastcheap
2nd Floor
London, EC3M1DT
United Kingdom

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