Discussion Papers, Department of Finance and Management Science, Norwegian School of Economics (NHH)
No 2005/12:
The perpetual American put option for jump-diffusions with applications
Knut K. Aase ()
Abstract: In this paper we solve an optimal stopping problem with an
infinite time horizon, when the state variable follows a jump-diffusion.
Under certain conditions our solution can be interpreted as the price of an
American perpetual put option, when the underlying asset follows this type
of process. We present several examples demonstrating when the solution can
be interpreted as a perpetual put price. This takes us into a study of how
to risk adjust jump-diffusions. One key observation is that the probability
distribution under the risk adjusted measure depends on the equity premium,
which is not the case for the standard, continuous version. This difference
may be utilized to find intertemporal, equilibrium equity premiums, for
example. Our basic solution is exact only when jump sizes can not be
negative. We investigate when our solution is an approximation also for
negative jumps. Various market models are studied at an increasing level of
complexity, ending with the incomplete model in the last part of the
paper.
Keywords: Optimal exercise policy; American put option; perpetual option; optimal stopping; incomplete markets; equity premiums; CCAPM.; (follow links to similar papers)
JEL-Codes: G00; (follow links to similar papers)
34 pages, November 30, 2005
Before downloading any of the electronic versions below
you should read our statement on
copyright.
Download GhostScript
for viewing Postscript files and the
Acrobat Reader for viewing and printing pdf files.
Full text versions of the paper:
1205.pdf 
Download Statistics
Questions (including download problems) about the papers in this series should be directed to Stein Fossen ()
Report other problems with accessing this service to Sune Karlsson ()
or Helena Lundin ().
Programing by
Design by Joachim Ekebom
