The Effect of Elliott Waves and Landau Damping on the Stability of Asset Pricing — A Case Study with the Crude Oil Prices

Abstract

The stability in stock markets is the theme of this work. It has been demonstrated that the random walk theory alone is insufficient to explain the dynamic behavior of asset or stock prices. Deviations from the random walk theory reveal collective behaviors that produce waves and patterns. Research has shown that the Fibonacci sequence and the golden ratio emerge in such dynamic systems, representing states of minimal stability. Their sustained stability is ensured by the presence of Landau damping within the system. The complex dynamics of the stock market can be analyzed by considering the exchanged shares as fluctuating and the unexchanged shares as nonfluctuating entities. The traders exhibit a kind of group oscillations that resemble the waves in physical plasma. At steady state, the waves can be expressed by a cosine term, and at the least stable state, the dynamics involves the golden ratio, such that the cosine of [Formula: see text] is equal to half of the golden ratio. Using the trigonometric cosine formula, it is possible to obtain other angles which are the multiples of [Formula: see text]. They can be expressed in terms of the golden ratio, and they stand as Fibonacci angles. The stabilization is achieved by a mechanism so-called Landau damping, and the waves thus created are called Elliott waves, and they keep the system near the instability border. It was found that these angles appear quite often in the motive and corrective Elliott waves in the weekly price change of crude oil between January 2001 and June 2023. The percent occurrence of these angles increases through oscillations in motive waves with peaks at 18°, [Formula: see text] and 72°. The corrective wave has a maximum peak at 36°, and the percent occurrence decreases through oscillations having smaller peak values at 54° and 72°. The highest values are such that the motive waves appear at 50% in the bull market, and the corrective waves at 27.8% in the bear market.