Asymptotic Solutions for Australian Options with Low Volatility

Sai Hung Marten Ting and Christian-Oliver Ewald

Applied Mathematical Finance, 2014, vol. 21, issue 6, 595-613

Abstract: In this paper we derive asymptotic expansions for Australian options in the case of low volatility using the method of matched asymptotics. The expansion is performed on a volatility scaled parameter. We obtain a solution that is of up to the third order. In case that there is no drift in the underlying, the solution provided is in closed form, for a non-zero drift, all except one of the components of the solutions are in closed form. Additionally, we show that in some non-zero drift cases, the solution can be further simplified and in fact written in closed form as well. Numerical experiments show that the asymptotic solutions derived here are quite accurate for low volatility.

Date: 2014
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DOI: 10.1080/1350486X.2014.906973

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