Strict local martingales and bubbles

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.

Published at http://dx.doi.org/10.1214/14-AAP1037 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• On optimal arbitrage
• A new kind of augmentation of filtrations suitable for a change of probability measure by a strict local martingale
• Call option prices based on Bessel processes

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