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Computational LPPL Fit to Financial Bubbles

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  • Vincenzo Liberatore
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    Abstract

    The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. If the on-going development of a bubble is suspected, asset prices can be fit numerically to the LPPL law. The best solutions can then indicate whether a bubble is in progress and, if so, the bubble critical time (i.e., when the bubble is expected to burst). Consequently, the LPPL model is useful only if the data can be fit to the model with algorithms that are accurate and computationally efficient. In this paper, we address primarily the computational efficiency and secondarily the precision of the LPPL non-linear least-square fit. Specifically, we present a parallel Levenberg-Marquardt algorithm (LMA) for LPPL least-square fit that sped up computation of more than a factor of four over a sequential LMA on historical and synthetic price series. Additionally, we isolate a linear sub-structure of the LPPL least-square fit that can be paired with an exact computation of the Jacobian, give new settings for the Levenberg-Marquardt damping factor, and describe a heuristic method to choose initial solutions.

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    File URL: http://arxiv.org/pdf/1003.2920
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1003.2920.

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    Date of creation: Mar 2010
    Date of revision: Jan 2011
    Handle: RePEc:arx:papers:1003.2920

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    Web page: http://arxiv.org/

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    1. Zhi-Qiang Jiang & Wei-Xing Zhou & Didier Sornette & Ryan Woodard & Ken Bastiaensen & Peter Cauwels, 2009. "Bubble Diagnosis and Prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Papers 0909.1007, arXiv.org, revised Oct 2009.
    2. Giovanni Dell'Ariccia & Olivier J. Blanchard & Paolo Mauro, 2010. "Rethinking Macroeconomic Policy," IMF Staff Position Notes 2010/03, International Monetary Fund.
    3. Didier Sornette & Ryan Woodard & Maxim Fedorovsky & Stefan Reimann & Hilary Woodard & Wei-Xing Zhou, 2009. "The Financial Bubble Experiment: advanced diagnostics and forecasts of bubble terminations," Papers 0911.0454, arXiv.org, revised May 2010.
    4. David S. Bree & Nathan Lael Joseph, 2010. "Fitting the Log Periodic Power Law to financial crashes: a critical analysis," Papers 1002.1010, arXiv.org, revised Apr 2013.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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