An explosion time characterization of asset price bubbles

• Published date: 01 June 2023
• Author: Robert A. Jarrow,Simon S. Kwok
• Date: 01 June 2023
• DOI: http://doi.org/10.1111/irfi.12404

SHORT REPORT

An explosion time characterization of asset price

bubbles

Robert A. Jarrow

1

| Simon S. Kwok

2

1

Samuel Curtis Johnson Graduate School of

Management, Cornell University, Ithaca,

New York, USA

2

School of Economics, The University of

Sydney, Sydney, New South Wales, Australia

Correspondence

Simon S. Kwok, School of Economics, The

University of Sydney, Sydney, NSW 2006,

Australia.

Email: simon.kwok@sydney.edu.au

Abstract

In a standard continuous time asset pricing model, this

paper provides an explosion time characterization of asset

price bubbles that extends the existing characterization the-

orems in the literature from diffusion processes to general

semimartingales (which can include jumps). This characteri-

zation has a nice economic interpretation, not emphasized

in the existing literature.

KEYWORDS

asset price bubble, explosion time, local volatility, quadratic

variation, risk-neutral probability measure, semimartingale

JEL CLASSIFICATION

G12

1|INTRODUCTION

The local martingale theory of bubbles was developed in a series of papers by Loewenstein and Willard (2000), Cox

and Hobson (2005), Heston et al. (2007), and Jarrow et al. (2007,2010). For a review of the local martingale theory

of bubble mathematics, see Protter (2013). Recent empirical evidence provides strong support for the usefulness of

this theory in practice, see Jarrow et al. (2011), Obayashi et al. (2017), Jarrow and Kwok (2021), and Choi and

Jarrow (2022).

Given a continuous time model on a filtered probability space in a frictionless, competitive, and arbitrage-free

market, the local martingale theory of bubbles characterizes a price bubble as a price process that is a strict local mar-

tingale and not a martingale under an equivalent local martingale probability measure. An equivalent local martingale

probability measure exists in such a setting by the first fundamental theorem of asset pricing. This is a nice

Received: 13 April 2022 Revised: 18 October 2022 Accepted: 7 November 2022

DOI: 10.1111/irfi.12404

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which

permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no

modifications or adaptations are made.

© 2022 The Authors. International Review of Finance published by John Wiley & Sons Australia, Ltd on behalf of International Review

of Finance Ltd.

International Review of Finance. 2023;23:469–479. wileyonlinelibrary.com/journal/irfi 469