Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T14:38:12.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Bounds for perpetual American option prices in a jump diffusion model

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Erik Ekström
Erik Ekström*
Affiliation:
University of Manchester
*
∗Postal address: School of Mathematics, University of Manchester, Sackville Street, Manchester M60 1QD, UK. Email address: ekstrom@maths.manchester.ac.uk
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.

We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black–Scholes model. We also investigate the dependence of the bounds on different parameters of the model.

Keywords

American optionboundjump diffusionoptimal stopping

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 867 - 873
Copyright
© Applied Probability Trust 2006 

References

Alvarez, L. H. R. (2003). On the properties of r-excessive mappings for a class of diffusions. Ann. Appl. Prob. 13, 1517–1533.CrossRefGoogle Scholar
Bellamy, N. and Jeanblanc, M. (2000). Incompleteness of markets driven by a mixed diffusion. Finance Stoch. 4, 209–222.CrossRefGoogle Scholar
Borodin, A. N. and Salminen, P. (2002). Handbook of Brownian Motion. Facts and Formulae, 2nd edn. Birkhäuser, Basel.CrossRefGoogle Scholar
Dayanik, S. and Karatzas, I. (2003). On the optimal stopping problem for one-dimensional diffusions. Stoch. Process. Appl. 107, 173–212.Google Scholar
Ekström, E. (2004). Properties of American option prices. Stoch. Process. Appl. 114, 265–278.CrossRefGoogle Scholar
Ekström, E. and Tysk, J. (2005). Properties of option prices in models with Jumps. Submitted.Google Scholar
Karatzas, I. and Shreve, S. (2000). Brownian Motion and Stochastic Calculus, 2nd edn. Springer, Berlin.Google Scholar
McKean, H. P. (1965). A free-boundary problem for the heat equation arising from a problem in mathematical economics. Industr. Manag. Rev. 6, 32–39.Google Scholar
Mordecki, E. (2002). Optimal stopping and perpetual options for Lévy processes. Finance Stoch. 6, 473–493.Google Scholar