Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session A22: Focus Session: Econophysics |
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Sponsoring Units: GSNP Chair: Victor Yakovenko, University of Maryland Room: Colorado Convention Center 108 |
Monday, March 5, 2007 8:00AM - 8:12AM |
A22.00001: Effect of citation patterns on network structure Soma Sanyal We propose a model for an evolving citation network that incorporates the citation pattern followed in a particular discipline. We define the citation pattern in a discipline by three factors. The average number of references per article, the probability of citing an article based on it's age and the number of citations it already has. We also consider the average number of articles published per year in the discipline. We propose that the probability of citing an article based on it's age can be modeled by a {\it lifetime distribution}. The lifetime distribution models the citation lifetime of an average article in a particular discipline. We find that the citation lifetime distribution in a particular discipline predicts the topological structure of the citation network in that discipline. We show that the power law exponent depends on the three factors that define the citation pattern. Finally we fit the data from the Physical Review D journal to obtain the citation pattern and calculate the total degree distribution for the citation network. [Preview Abstract] |
Monday, March 5, 2007 8:12AM - 8:24AM |
A22.00002: Counting solutions for the CDMA multiuser MAP demodulator Jun-ichi Inoue, J.P.L. Hatchett We evaluate the average number of locally minimal solutions for maximum-a-{\it posteriori} (MAP) demodulation in code-division multiple-access (CDMA) systems [1]. For this purpose, we use a sophisticated method to investigate the ground state properties for the Sherrington-Kirkpatrick-type (i.e. fully connected) spin glasses established by Tanaka and Edwards [2] in 1980. We derive the number of locally minimal solutions as a function of several parameters which specify the CDMA multiuser MAP demodulator. We also calculate the distribution function of the energies for the locally minimum states. We find that for a small number of chip intervals (or equivalently a large number of users) and large noise level at the base station, the number of local minimum solutions becomes larger than that of the SK model [3]. This provides us with useful information about the computational complexity of the MAP demodulator [4]. \\ \\ $[1]$ T. Tanaka, Europhys. Lett. {\bf 54} (4), 540 (2001). \\ $[2]$ F. Tanaka and S.F. Edwards, J. Phys. F: Metal Phys. {\bf 10} 2769 (1980). \\ $[3]$ D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. {\bf 35}, 1792 (1975). \\ $[4]$ J.P.L. Hatchett and J. Inoue, in preparation. [Preview Abstract] |
Monday, March 5, 2007 8:24AM - 8:36AM |
A22.00003: A Weibull distribution with power-law tails that describes the first passage time processes of foreign currency exchanges Naoya Sazuka, Jun-ichi Inoue A Weibull distribution with power-law tails is confirmed as a good candidate to describe the first passage time process of foreign currency exchange rates. The Lorentz curve and the corresponding Gini coefficient for a Weibull distribution are derived analytically. We show that the coefficient is in good agreement with the same quantity calculated from the empirical data. We also calculate the average waiting time which is an important measure to estimate the time for customers to wait until the next price change after they login to their computer systems. By assuming that the first passage time distribution might change its shape from the Weibull to the power-law at some critical time, we evaluate the averaged waiting time by means of the renewal-reward theorem. We find that our correction of tails of the distribution makes the averaged waiting time much closer to the value obtained from empirical data analysis. We also discuss the deviation from the estimated average waiting time by deriving the waiting time distribution directly. These results make us conclude that the first passage process of the foreign currency exchange rates is well described by a Weibull distribution with power-law tails. [Preview Abstract] |
Monday, March 5, 2007 8:36AM - 8:48AM |
A22.00004: A new perspective on Quantum Finance using the Black-Scholes pricing model Lamine Dieng Options are known to be divided into two types, the first type is called a call option and the second type is called a put option and these options are offered to stock holders in order to hedge their positions against risky fluctuations of the stock price. It is important to mention that due to fluctuations of the stock price, options can be found sometimes deep in the money, at the money and out of the money. A deep in the money option is described when the option's holder has a positive expected payoff, at the money option is when the option's holder has a zero expected payoff and an out of the money option is when the payoff is negative. In this work, we will assume the stock price to be described by the well known Black-Scholes model or sometimes called the multiplicative model. Using Ito calculus, Martingale and supermartingale theories, we investigated the Black-Scholes pricing equation at the money (X(stock price)= K (strike price)) when the expected payoff of the options holder is zero. We also hedged the Black-Scholes pricing equation in the limit when delta is zero to obtain the non-relativistic time independent Schroedinger equation in quantum mechanics. We compared the two equations and found the diffusion constant to be a function of the stock price in contrast to the Bachelier model we have worked on earlier. We solved the Schroedinger equation and found a dependence between interest rate, volatility and strike price at the money. [Preview Abstract] |
Monday, March 5, 2007 8:48AM - 9:00AM |
A22.00005: Evolution of Trading strategies Javier Vicente We attempt to classify the trading strategies of agents in the London Stock Exchange into broad categories. Our study is based on that that identifies the member of the exchange associated with each transaction. Based on the evolution of the inventory (holdings of the stock) as a function of time, we use clustering methods to classify the strategies into several groups. We study how these groups evolve in time and attempt to correlate the membership of the groups with other market properties, such as price volatility. [Preview Abstract] |
Monday, March 5, 2007 9:00AM - 9:12AM |
A22.00006: The Product Space and its Consequences for Economic Growth Cesar Hidalgo, Bailey Klinger, Albert-Laszlo Barabasi, Ricardo Hausmann In this paper, we test the assumption underlying the foundational models of trade that there always exist products through which countries can express their endowments and technology. We map the `space' of products in the world, and find it to be quite heterogeneous, with a central core and outer periphery. Moreover, we show that the way countries develop comparative advantage is far from random, and that the empirical rules observed herein predict, together with the structure of the product space, explain the lack of convergence in international income levels. Some developing countries produce in the periphery of the product space with few opportunities for diversification, whereas others have developed capabilities easily deployable in a wide range of products creating a path to convergence. [Preview Abstract] |
Monday, March 5, 2007 9:12AM - 9:24AM |
A22.00007: Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study Christian Silva, Victor Yakovenko We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades $N$ is found to be approximately Gaussian. The probability distribution of $N$ for a given time interval $\Delta t$ is non-Poissonian and has an exponential tail for large $N$ and a sharp cutoff for small $N$. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval $\Delta t$, which has exponential tails and a Gaussian central part, in agreement with empirical observations.\\ Reference: physics/0608299. [Preview Abstract] |
Monday, March 5, 2007 9:24AM - 10:00AM |
A22.00008: Using behavioral statistical physics to understand supply and demand Invited Speaker: We construct a quantitative theory for a proxy for supply and demand curves using methods that look and feel a lot like physics. Neoclassical economics postulates that supply and demand curves can be explained as the result of rational agents selfishly maximizing their utility, but this approach has had very little empirical success. We take quite a different approach, building supply and demand curves out of impulsive responses to not-quite-random trading fluctuations. Because of reasons of empirical measurability, as a good proxy for changes in supply and demand we study the aggregate price impact function $R(V)$, giving the average logarithmic price change $R$ as a function of the signed trading volume $V$. (If a trade $v_i$ is initiated by a buyer, it has a plus sign, and vice versa for sellers; the signed trading volume for a series of $N$ successive trades is $V_N(t) = \sum_{i=t}^{i=t+N} v_i$). We develop a ``zero-intelligence" null hypothesis that each trade $v_i$ gives an impulsive kick $f(v_i)$ to the price, so that the average return $R_N(t) = \sum_{i=t}^{i=t+N} f(v_i)$. Under the assumption that $v_i$ is IID, $R(V_N)$ has a characteristic concave shape, becoming linear in the limit as $N \to \infty$. Under some circumstances this is universal for large $N$, in the sense that it is independent of the functional form of $f$. While this null hypothesis gives useful qualitative intuition, to make it quantitatively correct, one must add two additional elements: (1) The signs of $v_i$ are a long-memory process and (2) the return $R$ is efficient, in the sense that it is not possible to make profits with a linear prediction of the signs of $v_i$. Using data from the London Stock Exchange we demonstrate that this theory works well, predicting both the magnitude and shape of $R(V_N)$. We show that the fluctuations in $R$ are very large and for some purposes more important than the average behavior. A computer model for the fluctuations suggests the existence of an equation of state relating the diffusion rate of prices to the flow of trading orders. [Preview Abstract] |
Monday, March 5, 2007 10:00AM - 10:12AM |
A22.00009: Modelling Limit Order Execution Times from Market Data Adlar Kim, Doyne Farmer, Andrew Lo Although the term ``liquidity'' is widely used in finance literatures, its meaning is very loosely defined and there is no quantitative measure for it. Generally, ``liquidity'' means an ability to quickly trade stocks without causing a significant impact on the stock price. From this definition, we identified two facets of liquidity -- 1.execution time of limit orders, and 2.price impact of market orders. The limit order is an order to transact a prespecified number of shares at a prespecified price, which will not cause an immediate execution. On the other hand, the market order is an order to transact a prespecified number of shares at a market price, which will cause an immediate execution, but are subject to price impact. Therefore, when the stock is liquid, market participants will experience quick limit order executions and small market order impacts. As a first step to understand market liquidity, we studied the facet of liquidity related to limit order executions -- execution times. In this talk, we propose a novel approach of modeling limit order execution times and show how they are affected by size and price of orders. We used q-Weibull distribution, which is a generalized form of Weibull distribution that can control the fatness of tail to model limit order execution times. [Preview Abstract] |
Monday, March 5, 2007 10:12AM - 10:24AM |
A22.00010: The Influence of Signed Order Volume on Stock Prices Austin Gerig, Doyne Farmer, Fabrizio Lillo, Szabolcs Mike Using data from the London Stock Exchange we investigate the influence of signed transaction order volume on current and future price changes. (Buy orders are given a positive sign, sell orders a negative sign). Empirical studies have shown that transaction order signs display long memory. Because buying tends to move the price up and selling tends to move the price down, this creates a puzzle regarding efficiency -- if transaction order signs are highly predictable, why aren't prices predictable? We show that efficiency is maintained by correlated fluctuations in the response of prices to orders. We also study whether or not this is an important effect causing clustered volatility in price changes, i.e. the tendency of the magnitude of price changes to be temporally correlated. [Preview Abstract] |
Monday, March 5, 2007 10:24AM - 10:36AM |
A22.00011: Is clustered volatility essential to understand heavy tails in financial markets? Anuj Purwar, J. Doyne Farmer Heavy tails are observed in the returns of stocks even for transaction by transaction data. We study the tail exponents and quantiles of the heavy tails for stock returns: first for transaction by transaction data, second after aggregating over $n$ transactions. In order to separate out the effect of clustered volatility, we repeat our analysis after shuffling the transaction sequence and look for variation in tail exponents and quantiles for shuffled vs. original (unshuffled) data. [Preview Abstract] |
Monday, March 5, 2007 10:36AM - 10:48AM |
A22.00012: Persistent Patterns in Trading Firms' Actions Neda Zamani, J. Doyne Farmer To understand the dynamics of price formation in financial markets, we take the approach of investigating the actions of market participants. We examine the impact of the participating firms on the price and find that different firms have different patterns of impact. Each firm can be representative of many traders with different trading habits and strategies but nevertheless we observe statistically significant differences in the firms' market impacts. We also investigate a method of clustering the firms based on a simplified conception of strategies. We find consistent clusters and patterns in firm strategies and show that these relations are statistically significant. [Preview Abstract] |
Monday, March 5, 2007 10:48AM - 11:00AM |
A22.00013: Universality of Tail Exponents of Price Changes? Luwen Huang, Doyne Farmer We study the tail exponents of the distribution of logarithmic price changes in financial markets, and investigate the conjecture that they are universal with an exponent near three. Using data from the London Stock Exchange, we construct the empirical distributions of price returns on several different time scales and study their variation as a function of parameters such as trading volume and tick size (the minimal unit of price variation). [Preview Abstract] |
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