Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-09T13:28:13.689Z Has data issue: false hasContentIssue false
  • English
  • Français

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

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

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Asmussen, S. (1987). Applied Probability and Queues, John Wiley, Chichester.Google Scholar
Asmussen, S., Glynn, P. and Pitman, J. (1995). Discretization error in simulation of one-dimensional reflecting Brownian motion. Ann. Appl. Prob. 5, 875–896.CrossRefGoogle Scholar
Bertoin, J. (1996). Lévy Processes. Cambridge University Press.Google Scholar
Broadie, M., Glasserman, P. and Kou, S. (1997). A continuity correction for discrete barrier options. Math. Finance 7, 325–349.CrossRefGoogle Scholar
Broadie, M., Glasserman, P. and Kou, S. G. (1999). Connecting discrete and continuous path-dependent options. Finance Stoch. 3, 55–82.Google Scholar
Cont, R. and Tankov, P. (2004). Financial Modelling with Jump Processes. Chapman & Hall/CRC, Boca Raton, FL.Google Scholar
Dia, E. H. A. (2010). Exotic options under exponential Lévy model. , Université Paris-Est. Available at http://tel.archives-ouvertes.fr/tel-00520583/.Google Scholar
Dia, E. H. A. and Lamberton, D. (2011). Continuity correction for barrier options in Jump-diffusion models. To appear in SIAM J. Financial Math.Google Scholar
Fuh, C.-D., Luo, S.-F. and Yen, J.-F. (2010). Pricing discrete path-dependent options under a Jump-diffusion model. In Seminars in Financial Statistics, Academia Sinica, 27 pp.Google Scholar
Gobet, E. and Menozzi, S. (2010). Stopped diffusion processes: boundary corrections and overshoot. Stoch. Process. Appl. 120, 130–162.Google Scholar
Knopp, K. (1990). Theory and Applications of Infinite Series. Dover, New York.Google Scholar
Sato, K. I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press.Google Scholar