On Peacocks and Lyrebirds: Australian Options, Brownian Bridges and the Average of Sub-Martingales

Abstract

There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. This is the peer reviewed version of the following article: Ewald, C.-O. and Yor, M. (2018) On peacocks and lyrebirds: Australian options, Brownian bridges, and the average of sub-martingales. Mathematical Finance, 28(2), pp. 536-549, which has been published in final form at http://dx. AbstractWe introduce a class of stochastic processes, which we refer to as lyrebirds. These extend a class of stochastic processes, which have recently been coined peacocks, but are more commonly known as processes which are increasing in the convex order. We show how these processes arise naturally in the context of Asian and Australian Options and consider further applications, such as the arithmetic average of a Brownian bridge and the average of sub-martingales, including the case of Asian and Australian options where the underlying features constant elasticity of variance (CEV) or is of Merton jump diffusion type.