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...

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 provides a solution for up to third order. In case that there is no drift in the underlying,...

We introduce a class of stochastic processes, which we refer to as Lyrebirds. These extend a class of stochastic processes, which have recently been coined as Peacocks, but are more commonly known as processes which are increasing in the convex order. We show how these processes arise naturally...