📝 Original Info
- Title: An empirical behavioral model of liquidity and volatility
- ArXiv ID: 0709.0159
- Date: 2008-12-02
- Authors: Researchers from original ArXiv paper
📝 Abstract
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are validated against real data. Our empirical studies of order flow uncover several interesting regularities in the way trading orders are placed and cancelled. The resulting simple model of order flow is used to simulate price formation under a continuous double auction, and the statistical properties of the resulting simulated sequence of prices are compared to those of real data. The model is constructed using one stock (AZN) and tested on 24 other stocks. For low volatility, small tick size stocks (called Group I) the predictions are very good, but for stocks outside Group I they are not good. For Group I, the model predicts the correct magnitude and functional form of the distribution of the volatility and the bid-ask spread, without adjusting any parameters based on prices. This suggests that at least for Group I stocks, the volatility and heavy tails of prices are related to market microstructure effects, and supports the hypothesis that, at least on short time scales, the large fluctuations of absolute returns are well described by a power law with an exponent that varies from stock to stock.
💡 Deep Analysis
Deep Dive into An empirical behavioral model of liquidity and volatility.
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are validated against real data. Our empirical studies of order flow uncover several interesting regularities in the way trading orders are placed and cancelled. The resulting simple model of order flow is used to simulate price formation under a continuous double auction, and the statistical properties of the resulting simulated sequence of prices are compared to those of real data. The model is constructed using one stock (AZN) and tested on 24 other stocks. For low volatility, small tick size stocks (called Group I) the predictions are very good, but for stocks outside Group I they are not good. For Group I, the model predicts the correct magnitude and functional form of the distribution of the volatility and the bid-ask spread, without adjusting any pa
📄 Full Content
In the last two decades the field of behavioral finance has presented many examples where equilibrium rational choice models are not able to explain real economic behavior 2 (Hirschleifer 2001, Barberis and Thaler 2003, Camerer 2003, Thaler 2005, Schleifer 2000). There are many efforts underway to build a foundation for economics directly based on psychological evidence, but this imposes a difficult hurdle for building quantitative theories. The human brain is a complex and subtle instrument, and in a general setting the distance from psychology to prices is large. In this study we take advantage of the fact that electronic markets provide a superb laboratory for studying patterns in human behavior. Market participants make decisions in an extremely complex environment, but in the end these decisions are reduced to the simple actions of placing and canceling trading orders. The data that we study contain tens of millions of records of trading orders and prices, allowing us to reconstruct the state of the market at any instant in time. We have a complete record of decision making outcomes in the context of the phenomenon we want to study, namely price formation. Within the domain where this model is valid, this allows us to make a simple but accurate model of the statistical properties of prices.
Our goal here is to capture behavioral regularities in order placement and cancellation, i.e. order flow, and to exploit these regularities to achieve a better understanding of liquidity and volatility. The practical component of this goal is to understand statistical properties of prices, such as the distribution of price returns and the bid-ask spread. We will use logarithmic returns r(t) = π m (t) -π m (t -1), where t is order placement time 3 and π m is the logarithmic midprice. The logarithmic midprice π m = 1/2(log p a (t) + log p b (t)), where p a (t) is the best selling price (best ask) and p b is the best buying price (best bid); on the rare occasions that we need a price rather than a logarithmic price, we will use p = exp(π m ). We are only interested in the size of price movements, and not in their direction. We will take the size of logarithmic returns |r(t)| as our proxy for volatility. Another important quantity is the bid ask spread s(t) = log p a (t) -log p b (t). The spread is important as a benchmark for transaction costs. A small market order to buy will execute at the best selling price, and a small order to sell will execute at the best buying price, so someone who first buys and then sells in close succession will pay the spread s(t). Our goal is to relate the magnitude and the distribution of volatility and the spread to statistical properties of order flow. The modeling task is to understand which properties of the order flow are important for understanding prices and to create a simple model for the relationship between them.
The model we develop here describes the endogenous dynamics of liquidity. We define liquidity as the difference between the current midprice and the price where an order of a given size can be executed. Previous work has shown that liquidity is typically the dominant determinant of volatility, at least for short time scales (Farmer et al. 2004, Weber and Rosenow 2006, Gillemot, Lillo and Farmer 2006). Periods of high volatility correspond to low liquidity and vice versa. Here we model the dynamics of the order book, i.e. we model fluctuations in liquidity, and use this to predict fluctuations in returns and spreads 4 . Thus understanding liquidity is the first and principal step to understanding volatility. 3 All results in this study are done in order placement time, i.e. we increment t → t + 1 just before each order placement occurs. There can be variable numbers of intervening cancellations. 4 Volatility in order placement time is essentially the same as in transaction time. Transaction time volatility typically gives a close approximation to real time volatility (Gillemot, Lillo and Farmer 2006).
Our model is based on a statistical description of the placement and cancellation of trading orders under a continuous double auction. This model follows in the footsteps of a long list of other models that have tried to describe order placement as a statistical process (Mendelson 1982 Smith et al. 2003). For a more detailed narrative of the history of this line of work, see Smith et al. (2003).
The model developed here was inspired by that of Daniels et al. (2003). The model of Daniels et al. was constructed to be solvable by making the assumption that limit orders, market orders, and cancellations can be described as independent Poisson processes. Because it assumes that order placement is random except for a few constraints, it can be regarded as a zero intelligence model of agent behavior. Although highly unrealistic in many respects, the zero intelligence model does a reasonable job of capturing the dynamic feedback and interaction between order placement on on
…(Full text truncated)…
📸 Image Gallery
Reference
This content is AI-processed based on ArXiv data.
