Published in:Research Paper Number: 238, Quantitative Finance Research Centre, University of Technology, Sydney
Extent:
1 Online-Ressource (35 p)
Language:
English
DOI:
10.2139/ssrn.2175896
Identifier:
Origination:
Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments December 1, 2008 erstellt
Description:
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