Algorithmic complexity theory and the relative efficiency of financial markets (original) (raw)

Efficiency of financial markets and algorithmic complexity

Journal of Physics: Conference Series, 2010

In this work we are interested in the concept of market efficiency and its relationship with the algorithmic complexity theory. We employ a methodology based on the Lempel-Ziv index to analyze the relative efficiency of high-frequency data coming from the Brazilian stock market.

The relative efficiency of stockmarkets

2008

Financial economists usually assess market efficiency in absolute terms. This is a shortcoming. One way of dealing with the relative efficiency of markets is to resort to the efficiency interpretation provided by algorithmic complexity theory. This paper employs such an approach in order to rank 36 stock exchanges and 37 individual company stocks in terms of their relative efficiency.

Complexity analysis of the stock market

Physica A: Statistical Mechanics and its Applications, 2007

We study the complexity of the stock market by constructing -machines of Standard and Poor's 500 index from February 1983 to April 2006 and by measuring the statistical complexities. It is found that both the statistical complexity and the number of causal states of constructed -machines have decreased for last 20 years and that the average memory length needed to predict the future optimally has become shorter. These results support that the information is delivered to the economic agents and applied to the market prices more rapidly in year 2006 than in year 1983. r

Algorithmic Complexity of Real Financial Markets

Physica A: Statistical Mechanics and its Applications, 2001

A new approach to the understanding of complex behavior of financial markets index using tools from thermodynamics and statistical physics is developed. Physical complexity, a quantity rooted in the Kolmogorov–Chaitin theory is applied to binary sequences built up from real time series of financial markets indexes.The study is based on NASDAQ and Mexican IPC data. Different behaviors of this quantity are shown when applied to the intervals of series placed before crashes and to intervals when no financial turbulence is observed. The connection between our results and the effcient market hypothesis is discussed.

Levels of complexity in financial markets

Physica A: Statistical Mechanics and its Applications, 2001

We consider different levels of complexity which are observed in the empirical investigation of financial time series. We discuss recent empirical and theoretical work showing that statistical properties of financial time series are rather complex under several ways. Specifically, they are complex with respect to their (i) temporal and (ii) ensemble properties. Moreover, the ensemble return properties show a behavior which is specific to the nature of the trading day reflecting if it is a normal or an extreme trading day.

A computational view of market efficiency

Quantitative Finance, 2011

We propose to study market efficiency from a computational viewpoint. Borrowing from theoretical computer science, we define a market to be efficient with respect to resources S (e.g., time, memory) if no strategy using resources S can make a profit. As a first step, we consider memory-m strategies whose action at time t depends only on the m previous observations at times t − m,. .. , t − 1. We introduce and study a simple model of market evolution, where strategies impact the market by their decision to buy or sell. We show that the effect of optimal strategies using memory m can lead to "market conditions" that were not present initially, such as (1) market bubbles and (2) the possibility for a strategy using memory m ′ > m to make a bigger profit than was initially possible. We suggest ours as a framework to rationalize the technological arms race of quantitative trading firms.

Increasing market efficiency in the stock markets

The European Physical Journal B, 2008

We study the temporal evolutions of three stock markets; Standard and Poor's 500 index, Nikkei 225 Stock Average, and the Korea Composite Stock Price Index. We observe that the probability density function of the log-return has a fat tail but the tail index has been increasing continuously in recent years. We have also found that the variance of the autocorrelation function, the scaling exponent of the standard deviation, and the statistical complexity decrease, but that the entropy density increases as time goes over time. We introduce a modified microscopic spin model and simulate the model to confirm such increasing and decreasing tendencies in statistical quantities. These findings indicate that these three stock markets are becoming more efficient.

Theoretical and Methodological Proposals Regarding the Informational Efficiency of Financial Markets

2015

The efficient market theory has given rise to numerous controversies which have further generated new research trends, some focusing on complex mathematical models, whereas others focusing on different hypotheses of financial markets approached form completely new perspectives. In this article, we present the new paradigms in the field of financial market efficiency, such as: the Adaptive Market Hypothesis, the Noisy Market Hypothesis, the Fractal Market Hypothesis and the Behavioural Finance. Also, we analyse the effects of fractal market hypothesis and of behavioural finance on emerging capital markets.