Gaussian and non-Gaussian models for financial bubbles via econophysics
AbstractWe 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 rise 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 seen to represent a phase transition from stochastic to deterministic behaviour in prices. Our approach is first illustrated by a benchmark Gaussian model - subsequently extended to a heavy-tailed model based on the Normal Inverse Gaussian distribution. 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 27307.
Date of creation: 08 Dec 2010
Date of revision:
financial crashes; super-exponential growth; illusion of certainty; bubbles; heavy tails;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-12-18 (All new papers)
- NEP-ORE-2010-12-18 (Operations Research)
- NEP-RMG-2010-12-18 (Risk Management)
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