On peacocks and lyrebirds: Australian options, Brownian bridges, and the average of sub-martingales

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. (doi: 10.1111/mafi.12144)

Abstract

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 peacocks, but are more commonly known as processes that 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 submartingales, including the case of Asian and Australian options where the underlying features constant elasticity of variance or is of Merton jump diffusion type.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ewald, Professor Christian
• Authors: Ewald, C.-O., and Yor, M.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Mathematical Finance
• Publisher: Wiley
• ISSN: 0960-1627
• ISSN (Online): 1467-9965
• Published Online: 18 April 2017
• Copyright Holders: Copyright © 2017 Wiley Periodicals, Inc.
• First Published: First published in Mathematical Finance 28(2):536-549
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher