Gaussian and non-Gaussian models for financial bubbles via econophysics

Fry, John

Abstract

We develop a rational expectations model of financial bubbles and study how the risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model: namely, that the price must raise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an illusion of certainty as described by a decreasing volatility function. As the volatility function decreases crashes can be explicitly seen to represent a phase transition from stochastic to deterministic behaviour in prices. Our approach is first illustrated by a benchmark Gaussian model, which we subsequently extend to a heavy-tailed model based on the Normal Inverse Gaussian distribution in order to provide a better fit to empirical financial data. Our model is illustrated by an empirical application to the London Stock Exchange. Results suggest that the aftermath of the Bank of England's process of quantitative easing has coincided with a bubble in the FTSE 100.

Citation

Fry, J. (2011). Gaussian and non-Gaussian models for financial bubbles via econophysics. Hyperion International Journal of Econophysics and New Economy, 4(1), 7-22

• Journal Article Type: Article
• Publication Date: 2011
• Deposit Date: Feb 4, 2022
• Publicly Available Date: Mar 9, 2022
• Journal: Hyperion International Journal of Econophysics and New Economy
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 1
• Pages: 7-22
• Keywords: Financial crashes; Super-exponential growth; Illusion of certainty; Heavy tails; Bubbles
• Public URL: https://hull-repository.worktribe.com/output/3920978
• Publisher URL: https://www.journal-hyperion.ro/journal-archive/category/7-volume-4-issue-1-2011