EconPapers    
Economics at your fingertips  
 

A Visual Classification of Local Martingales

Hardy Hulley and Eckhard Platen ()

No 238, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper considers the problem of when a local martingale is a martingale or a universally integrable martingale, for the case of time-homogeneous scalar diffusions. Necessary and suffcient conditions of a geometric nature are obtained for answering this question. These results are widely applicable to problems in stochastic finance. For example, in order to apply risk-neutral pricing, one must first check that the chosen density process for an equivalent change of probability measure is in fact a martingale. If not, risk-neutral pricing is infeasible. Furthermore, even if the density process is a martingale, the possibility remains that the discounted price of some security could be a strict local martingale under the equivalent risk-neutral probability measure. In this case, well-known identities for option prices, such as put-call parity, may fail. Using our results, we examine a number of basic asset price models, and identify those that suffer from the above-mentioned difficulties.

Keywords: diffusions; first-passage times; Laplace transforms; local martingales; ordinary differential equations (search for similar items in EconPapers)
Date: 2008-12-01
References: Add references at CitEc
Citations View citations in EconPapers (3) Track citations by RSS feed

Downloads: (external link)
https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp238.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

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:uts:rpaper:238

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().

 
Page updated 2018-10-13
Handle: RePEc:uts:rpaper:238