Efficient Simulation of the Multi Asset Heston Model

19 Pages Posted: 11 Feb 2016 Last revised: 15 Feb 2016

See all articles by Marco de Innocentis

Marco de Innocentis

Credit Suisse Securities (Europe) Limited; University of Leicester

Roland Lichters

Quaternion Risk Management

Markus Trahe

Credit Suisse AG

Date Written: February 8, 2016

Abstract

This paper describes a procedure for efficiently simulating a multi asset Heston model with an arbitrary correlation structure. Very little literature can be found on the topic (e.g. Wadman (2010) and Dimitroff et al. (2011)), the latter being very restrictive on correlation assumptions. The scheme proposed in this text is based on Andersen's Quadratic Exponential (QE) scheme (2008) and operates with an arbitrary input correlation structure, which is partially decorrelated via a Gaussian copula approach to fit the single asset QE prerequisites. Given a long term horizon, it is shown numerically that, in the multi asset QE (MQE) scheme, all combinations of terminal correlations converge quickly to the true terminal correlations for decreasing Monte Carlo time step size, if the input correlation matrix is interpreted as the system's instantaneous correlation matrix. Convergence of vanilla and spread option prices is investigated, in order to verify the appropriate behaviour for higher moments of the marginal and the joint distribution under MQE. Finally, the superiority of MQE vs. Taylor based schemes is shown by comparing convergence of the empirical PDF, calculated with Monte Carlo, to the "exact" function calculated via Fourier inversion.

Keywords: Heston, multi asset, Monte Carlo, efficient simulation, numerical scheme, option pricing

JEL Classification: G12, C63

Suggested Citation

de Innocentis, Marco and Lichters, Roland and Trahe, Markus, Efficient Simulation of the Multi Asset Heston Model (February 8, 2016). Available at SSRN: https://ssrn.com/abstract=2729475 or http://dx.doi.org/10.2139/ssrn.2729475

Marco De Innocentis

Credit Suisse Securities (Europe) Limited ( email )

1 Cabot Square
London, E14 4QJ
United Kingdom

University of Leicester ( email )

Department of Mathematics
University Road
Leicester, LE1 7RG
United Kingdom

Roland Lichters

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

Markus Trahe (Contact Author)

Credit Suisse AG ( email )

Uetlibergstrasse 231
Zürich, 8045
Switzerland

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