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

Christian-Oliver Ewald, University of Glasgow, Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance
Marc Yor, Université Paris VI Pierre et Marie Curie


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CHRISTIAN-OLIVER EWALD, University of Glasgow, Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance
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MARC YOR, Université Paris VI Pierre et Marie Curie
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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 in the context of Asian and Australian Options and consider further interesting applications, such as the arithmetic average of a Brownian bridge and the average of sub-martingales, including the case of Asian options where the underlying features constant elasticity of variance (CEV).

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