The Annals of Applied Probability

Strict local martingales and bubbles

Constantinos Kardaras, Dörte Kreher, and Ashkan Nikeghbali

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Abstract

This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine the “default term” apparent in risk-neutral option prices if the underlying stock exhibits a bubble modeled by a strict local martingale. Results for certain path dependent options and last passage time formulas are given.

Article information

Source
Ann. Appl. Probab., Volume 25, Number 4 (2015), 1827-1867.

Dates
Received: December 2013
First available in Project Euclid: 21 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1432212431

Digital Object Identifier
doi:10.1214/14-AAP1037

Mathematical Reviews number (MathSciNet)
MR3348996

Zentralblatt MATH identifier
1336.91076

Subjects
Primary: 91G99: None of the above, but in this section 60G30: Continuity and singularity of induced measures 60G44: Martingales with continuous parameter 91G20: Derivative securities

Keywords
Strict local martingales bubbles

Citation

Kardaras, Constantinos; Kreher, Dörte; Nikeghbali, Ashkan. Strict local martingales and bubbles. Ann. Appl. Probab. 25 (2015), no. 4, 1827--1867. doi:10.1214/14-AAP1037. https://projecteuclid.org/euclid.aoap/1432212431


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