Strong Bubbles and Strict Local Martingales

38 Pages Posted: 21 Feb 2015 Last revised: 9 Feb 2016

See all articles by Martin Herdegen

Martin Herdegen

University of Warwick - Department of Statistics

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Date Written: January 29, 2016

Abstract

In a numéraire-independent framework, we study a financial market with N assets which are all treated in a symmetric way. We define the fundamental value *S of an asset S as its superreplication price and say that the market has a strong bubble if *S and S deviate from each other. None of these concepts needs any mention of martingales. Our main result then shows that under a weak absence-of-arbitrage assumption (basically NUPBR), a market has a strong bubble if and only if in all numéraires for which there is an equivalent local martingale measure (ELMM), asset prices are strict local martingales under all possible ELMMs. We show by an example that our bubble concept lies strictly between the existing notions from the literature. We also give an example where asset prices are strict local martingales under one ELMM, but true martingales under another, and we show how our approach can lead naturally to endogenous bubble birth.

Note: This paper is a thoroughly revised and rewritten version of an earlier preprint which circulated under the title ”Economics-Based Financial Bubbles (and Why They Imply Strict Local Martingales)“.

Keywords: financial bubble, incomplete financial market, fundamental value, superreplication, strict local martingale, numéraire, viability, efficiency, no dominance efficiency, no dominance

JEL Classification: G10, C60

Suggested Citation

Herdegen, Martin and Schweizer, Martin, Strong Bubbles and Strict Local Martingales (January 29, 2016). International Journal of Theoretical and Applied Finance, Forthcoming, Swiss Finance Institute Research Paper No. 15-05, Available at SSRN: https://ssrn.com/abstract=2566815 or http://dx.doi.org/10.2139/ssrn.2566815

Martin Herdegen

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

Martin Schweizer (Contact Author)

ETH Zurich ( email )

Mathematik, HG G51.2
Raemistrasse 101
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
239
Abstract Views
1,167
rank
147,390
PlumX Metrics