Financial Bubbles

Chapter 1

Financial Bubbles

Efsun K¨ r¨ m, Gerhard-Wilhelm Weber and Cem ˙ un uu Iyig¨

Abstract We study on speculative financial bubbles whose characteristic can be modeled by Log Periodic Power Law (LPPL) which is represented by D. Sornette and his colleagues. The most probable time of the crash is estimated by a parameter in the equation. All parameters used in the equation, are forecasted by optimization through a genetic algorithm. Analysis of a time series by S&P 500 from 1987 shows the signals of the LPPL before the financial crisis of October 1987. In addition to the speculative bubbles, we also present and investigate antibubbles. They, likewise speculative bubbles, also follow log-periodic power law but, of course, with decelerating oscillations and, generally, in a bearish way inclined instead of a bullish way. We also introduce an alternative method which approaches the bubble concept geometrically and benefits from the advantages of optimization and machine learning. Keywords: Financial mathematics, bubble, Log-periodic power law, optimization, fitting, prediction.

1.1 Introduction

Basically, financial bubbles are artificial increases in price which are created by high expectations of individuals; in other words, artificial price augmentation originated from greediness of human beings. Since some investors do not know how to manage their risk when the bubbles burst, this causes big disappointment resulting even in

Efsun K¨ r¨ m uu Institute of Applied Mathematics, METU, 06531 Ankara, Turkey, e-mail: efsun.kurum@gmail.com Gerhard-Wilhelm Weber Institute of Applied Mathematics, METU, 06531 Ankara, Turkey, e-mail: gweber@metu.edu.tr Cem ˙ un Iyig¨ Department of Industrial Engineering, METU, 06531 Ankara, Turkey, e-mail: iyigun@metu.edu.tr

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Efsun K¨ r¨ m, Gerhard-Wilhelm Weber and Cem ˙ un uu Iyig¨

committing suicide. Moreover, their results affect the whole world like prompting domino stones. For instance, because of the recent...