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Connecting discrete and continuous lookback or hindsight options in exponential Lévy models

Part of: Markov processes Mathematical finance Partial differential equations, boundary value problems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

E. H. A. Dia  and
D. Lamberton
E. H. A. Dia*
Affiliation:
Université Paris-Est
D. Lamberton*
Affiliation:
Université Paris-Est
*
∗ Postal address: Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR CNRS 8050, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée, France.
∗ Postal address: Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR CNRS 8050, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée, France.
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Abstract

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Motivated by the pricing of lookback options in exponential Lévy models, we study the difference between the continuous and discrete supremums of Lévy processes. In particular, we extend the results of Broadie, Glasserman and Kou (1999) to jump diffusion models. We also derive bounds for general exponential Lévy models.

Keywords

Exponential Lévy modellookback optioncontinuity correction

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 60J75: Jump processes 65N15: Error bounds
Secondary: 91G20: Derivative securities
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011 , pp. 1136 - 1165
Copyright
Copyright © Applied Probability Trust 2011 

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