arXiv subjects

Austin Gerig

Publications and source records attributed to Austin Gerig.

15 recordsLinked to original sources

arXiv2014

Are There Many Worlds?

It is often thought that the existence of other worlds cannot be scientifically verified and therefore should be treated as philosophical speculation. In this article, I describe several methods for determining if other worlds exist, even without interacting with them. These methods are based on the following premise: if there are many worlds, then the statistical properties of a natural process are biased when measured by an observer whose existence was influenced by the process. The bias is always in the same direction, making the process appear more beneficial for the existence of the observer than it actually is. I suggest several potential ways of measuring the bias, show through a simple model of population dynamics how the bias is generated, and briefly consider whether our current drop in population growth is evidence of many worlds.

physics.hist-ph↗

arXiv2013

Simulating the Synchronizing Behavior of High-Frequency Trading in Multiple Markets

Nearly one-half of all trades in financial markets are executed by high-speed, autonomous computer programs -- a type of trading often called high-frequency trading (HFT). Although evidence suggests that HFT increases the efficiency of markets, it is unclear how or why it produces this outcome. Here we create a simple model to study the impact of HFT on investors who trade similar securities in different markets. We show that HFT can improve liquidity by allowing more transactions to take place without adversely affecting pricing or volatility. In the model, HFT synchronizes the prices of the securities, which allows buyers and sellers to find one another across markets and increases the likelihood of competitive orders being filled.

q-fin.TR↗

arXiv2013

A Stochastic Feedback Model for Volatility

Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer timescales, strong autocorrelations in absolute returns but zero autocorrelation in returns themselves, and multifractal scaling. Although the underlying cause of these features is unknown, there is growing evidence they originate in the behavior of volatility, i.e., in the behavior of the magnitude of price fluctuations. In this paper, we posit a feedback mechanism for volatility that closely reproduces the non-trivial properties of empirical prices. The model is parsimonious, contains only two parameters that are easily estimated, fits empirical data better than standard models, and can be grounded in a straightforward framework where volatility fluctuations are driven by the estimation error of an exogenous Poisson rate.

q-fin.ST↗

arXiv2013

Universal Doomsday: Analyzing Our Prospects for Survival

Given a sufficiently large universe, numerous civilizations almost surely exist. Some of these civilizations will be short-lived and die out relatively early in their development, i.e., before having the chance to spread to other planets. Others will be long-lived, potentially colonizing their galaxy and becoming enormous in size. What fraction of civilizations in the universe are long-lived? The "universal doomsday" argument states that long-lived civilizations must be rare because if they were not, we should find ourselves living in one. Furthermore, because long-lived civilizations are rare, our civilization's prospects for long-term survival are poor. Here, we develop the formalism required for universal doomsday calculations and show that while the argument has some force, our future is not as gloomy as the traditional doomsday argument would suggest, at least when the number of early existential threats is small.

astro-ph.CO↗

arXiv2012

High-Frequency Trading Synchronizes Prices in Financial Markets

High-speed computerized trading, often called "high-frequency trading" (HFT), has increased dramatically in financial markets over the last decade. In the US and Europe, it now accounts for nearly one-half of all trades. Although evidence suggests that HFT contributes to the efficiency of markets, there are concerns it also adds to market instability, especially during times of stress. Currently, it is unclear how or why HFT produces these outcomes. In this paper, I use data from NASDAQ to show that HFT synchronizes prices in financial markets, making the values of related securities change contemporaneously. With a model, I demonstrate how price synchronization leads to increased efficiency: prices are more accurate and transaction costs are reduced. During times of stress, however, localized errors quickly propagate through the financial system if safeguards are not in place. In addition, there is potential for HFT to enforce incorrect relationships between securities, making prices more (or less) correlated than economic fundamentals warrant. This research highlights an important role that HFT plays in markets and helps answer several puzzling questions that previously seemed difficult to explain: why HFT is so prevalent, why HFT concentrates in certain securities and largely ignores others, and finally, how HFT can lower transaction costs yet still make profits.

q-fin.TR↗

arXiv2012

The Doomsday Argument in Many Worlds

You and I are highly unlikely to exist in a civilization that has produced only 70 billion people, yet we find ourselves in just such a civilization. Our circumstance, which seems difficult to explain, is easily accounted for if (1) many other civilizations exist and if (2) nearly all of these civilizations (including our own) die out sooner than usually thought, i.e., before trillions of people are produced. Because the combination of (1) and (2) make our situation likely and alternatives do not, we should drastically increase our belief that (1) and (2) are true. These results follow immediately when considering a many worlds version of the "Doomsday Argument" and are immune to the main criticism of the original Doomsday Argument.

physics.pop-ph↗

arXiv2011

How efficiency shapes market impact

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e., the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two thirds of peak impact.

q-fin.TR↗

arXiv2010

Automated Liquidity Provision and the Demise of Traditional Market Making

Traditional market makers are losing their importance as automated systems have largely assumed the role of liquidity provision in markets. We update the model of Glosten and Milgrom (1985) to analyze this new world: we add multiple securities and introduce an automated market maker who uses the relationships between securities to price order flow. This new automated participant transacts the majority of orders, sets prices that are more efficient, and increases informed and decreases uninformed traders' transaction costs. These results can explain the recent dominance of high frequency trading in US markets and the corresponding increase in trading volume and decrease in transaction costs for US stocks.

q-fin.TR↗

arXiv2010

Universal Laws and Economic Phenomena

This is a short commentary piece that discusses how the methods used in the natural sciences can apply to economics in general and financial markets specifically.

q-fin.GN↗

arXiv2009

Universal Behavior of Extreme Price Movements in Stock Markets

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.

q-fin.ST↗

arXiv2009

Market impact and trading profile of large trading orders in stock markets

We empirically study the market impact of trading orders. We are specifically interested in large trading orders that are executed incrementally, which we call hidden orders. These are reconstructed based on information about market member codes using data from the Spanish Stock Market and the London Stock Exchange. We find that market impact is strongly concave, approximately increasing as the square root of order size. Furthermore, as a given order is executed, the impact grows in time according to a power-law; after the order is finished, it reverts to a level of about 0.5-0.7 of its value at its peak. We observe that hidden orders are executed at a rate that more or less matches trading in the overall market, except for small deviations at the beginning and end of the order.

q-fin.TR↗

arXiv2009

Model for Non-Gaussian Intraday Stock Returns

Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape, and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday, but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.

q-fin.ST↗

arXiv2008

A Theory for Market Impact: How Order Flow Affects Stock Price

It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the market impact of hidden orders (orders that reflect the true intention of buying and selling) that matches the empirically measured result and that reproduces some of the non-trivial and universal properties of stock returns (returns are percent changes in stock price). The theory is based on a simple premise, that the stock market can be modeled in a mechanical way - as a device that translates order flow into an uncorrelated price stream. Given that order flow is highly autocorrelated, this premise requires that market impact (1) depends on past order flow and (2) is asymmetric for buying and selling. I derive the specific form for the dependence in (1) by assuming that current liquidity responds to information about all currently active hidden orders (liquidity is a measure of the price response to a transaction of a given size). This produces an equation that suggests market impact should scale logarithmically with total order size. Using data from the London Stock Exchange I empirically measure market impact and show that the result matches the theory. Also using empirical data, I qualitatively specify the asymmetry of (2). Putting all results together, I form a model for market impact that reproduces three universal properties of stock returns - that returns are uncorrelated, that returns are distributed with a power law tail, and that the magnitude of returns is highly autocorrelated (also known as clustered volatility).

q-fin.ST↗

arXiv2007

Chaos in a one-dimensional compressible flow

We study the dynamics of a one-dimensional discrete flow with open boundaries - a series of moving point particles connected by ideal springs. These particles flow towards an inlet at constant velocity, pass into a region where they are free to move according to their nearest neighbor interactions, and then pass an outlet where they travel with a sinusoidally varying velocity. As the amplitude of the outlet oscillations is increased, we find that the resident time of particles in the chamber follows a bifurcating (Feigenbaum) route to chaos. This irregular dynamics may be related to the complex behavior of many particle discrete flows or is possibly a low-dimensional analogue of non-stationary flow in continuous systems.

nlin.CD↗

arXiv2006

Market efficiency and the long-memory of supply and demand: Is price impact variable and permanent or fixed and temporary?

In this comment we discuss the problem of reconciling the linear efficiency of price returns with the long-memory of supply and demand. We present new evidence that shows that efficiency is maintained by a liquidity imbalance that co-moves with the imbalance of buyer vs. seller initiated transactions. For example, during a period where there is an excess of buyer initiated transactions, there is also more liquidity for buy orders than sell orders, so that buy orders generate smaller and less frequent price responses than sell orders. At the moment a buy order is placed the transaction sign imbalance tends to dominate, generating a price impact. However, the liquidity imbalance rapidly increases with time, so that after a small number of time steps it cancels all the inefficiency caused by the transaction sign imbalance, bounding the price impact. While the view presented by Bouchaud et al. of a fixed and temporary bare price impact is self-consistent and formally correct, we argue that viewing this in terms of a variable but permanent price impact provides a simpler and more natural view. This is in the spirit of the original conjecture of Lillo and Farmer, but generalized to allow for finite time lags in the build up of the liquidity imbalance after a transaction. We discuss the possible strategic motivations that give rise to the liquidity imbalance and offer an alternative hypothesis. We also present some results that call into question the statistical significance of large swings in expected price impact at long times.

physics.soc-ph↗