Carlos Ibarra-Valdez

Multifractal Hurst analysis of crude oil prices

Daily records of international crude oil prices are studied using multifractal analysis methods. Rescaled range Hurst analysis provides evidence that the crude oil market is a persistent process with long-run memory effects. On the other hand, height–height correlation analysis reveals evidence of multifractal structures in the sense that the crude oil dynamics displays mixing of (rough) Hurst exponents. The existence of two characteristic time scales in the order of weeks and quarters is discovered and the corresponding prices dynamics are extracted using moving-average-based filtering. These results seem to demonstrate that the crude oil market is consistent with the random-walk assumption only at time scales of the order of days to weeks. A plausible oil price formation mechanism is discussed in terms of the market dynamics at three different time scales.

Modeling stock market dynamics based on conservation principles

In this paper, a deterministic framework for modeling stock market dynamics is presented. The model is based on assets conservation principles and consists of a series of differential equations describing the dynamics of assets trading, and a (nonlinear) functional equation describing trade conservation (i.e., what is bought (sold) by one trader is sold (bought) by other traders). In this way, the dynamics of the assets and its price are determined by the trading dynamics. An equilibrium price is achieved when certain demand/supply equations are satisfied. Attention is devoted to a specific case, in which the trading activity is based on trader groups and an infinitely divisible asset. Numerical simulations show that even a single stock market asset with two classes of investors can display oscillatory price dynamics and instability. Moreover, the underlying oscillatory time-series display a discontinuous erratic-type behavior.

Technical trading can induce long-run memory in financial markets

A simple agent-based model is used to propose an explanation of the source of long-run memory in financial markets. It is shown that the resulting model is equivalent to a neutral-type differential equation in the price dynamics, which displays a persistence property that can be related to memory effects.

COMPLEX DYNAMICS IN A SIMPLE STOCK MARKET MODEL

A deterministic model is introduced in terms of conservation principles to describe the (qualitative) price dynamics of a stock market. It is shown how the fundamentalist and chartist patterns of the trader behavior affect the price dynamics. The model can display complex oscillatory behavior with transient erratic oscillations, which resembles the behavior found in actual price dynamics. By means of numerical simulations, it is shown that the model can produce price time-series with statistics similar to that found in real financial data.