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2015•The Annals of Applied ProbabilityOpen access

Strict local martingales and bubbles

Constantinos Kardaras, Dörte Kreher, 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.

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What this paper is about

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.

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OpenAlex reports 45 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Local martingale, Martingale pricing, Martingale (probability theory), Mathematical finance, Economics, Mathematical economics, Econometrics, Mathematics

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