The perpetual American put option for jump-diffusions: Implications for equity premiums

Knut Aase

No 2004/19, Discussion Papers from Norwegian School of Economics, Department of Business and Management Science

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.

The probability distribution under the risk adjusted measure turns out to depend on the equity premium, which is not the case for the standard, continuous version. This difference is utilized to find intertemporal, equilibrium equity premiums.

We apply this technique to the US equity data of the last century, and find an indication that the risk premium on equity was about two and a half per cent if the risk free short rate was around one per cent. On the other hand, if the latter rate was about four per cent, we similarly find that this corresponds to an equity premium of around four and a half per cent.

The advantage with our approach is that we need only equity data and option pricing theory, no consumption data was necessary to arrive at these conclusions.

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 (search for similar items in EconPapers)
JEL-codes: D52 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2004-12-17
New Economics Papers: this item is included in nep-cfn
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/11250/163726 (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://hdl.handle.net/11250/163726 [302 Found]--> https://www.unit.no/brage-denne-lenken-er-ikke-lenger-gyldig [301 Moved Permanently]--> https://sikt.no/brage-denne-lenken-er-ikke-lenger-gyldig)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hhs:nhhfms:2004_019

Access Statistics for this paper

More papers in Discussion Papers from Norwegian School of Economics, Department of Business and Management Science NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway. Contact information at EDIRC.
Bibliographic data for series maintained by Stein Fossen ().