Asian and Australian options: A common perspective

Posted: 9 Sep 2009 Last revised: 17 Sep 2013

See all articles by Christian-Oliver Ewald

Christian-Oliver Ewald

University of Glasgow; Høgskole i Innlandet

Olaf Menkens

Dublin City University - School of Mathematical Sciences

Sai Hung Marten Ting

The University of Sydney

Date Written: November 9, 2011

Abstract

We show that Australian options are equivalent to fixed or floating strike Asian options and consequently that by studying Asian options from the Australian perspective and vice versa, much can be gained. One specific application of this "Australian Approach" leads to a natural dimension reduction for the pricing PDE of Asian options, with or without stochastic volatility, featuring time independent coefficients. Another application lies in the improvement of Monte Carlo schemes, where the "Australian Approach" results in a path-independent method. We also show how the Milevsky and Posner (1998) result on the reciprocal $\Gamma$-approximation for Asian options can be quickly obtained by using the connection to Australian options. Further, we present an analytical (exact) pricing formula for Australian options and adapt a result of Carr, Ewald and Xiao (2008) to show that the price of an Australian option is increasing in the volatility and by doing this answering a standing question by Moreno and Navas (2008).

Keywords: Asset pricing, Derivatives, Asian Options, Numerical Methods

JEL Classification: G12, G13, C63

Suggested Citation

Ewald, Christian-Oliver and Menkens, Olaf and Ting, Sai Hung Marten, Asian and Australian options: A common perspective (November 9, 2011). Journal of Economic Dynamics and Control, Vol. 37, No. 5, 2013, Available at SSRN: https://ssrn.com/abstract=1469136 or http://dx.doi.org/10.2139/ssrn.1469136

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Høgskole i Innlandet ( email )

Lillehammer, 2624
Norway

Olaf Menkens

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

Sai Hung Marten Ting

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

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