dyamics of quote prices in artificial mkts

7/31/2019 Dyamics of Quote Prices in Artificial Mkts

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allocations. At each instant in time, the probability of entering the market is an

increasing function of the distance of the agents current portfolio from the opti-mal allocation of wealth. Once an agent is selected to enter the market, the agents

ability to make his desired trades effective depends on the state of the order book.

We fix the order type submission strategy: all agents submit a market order for the

quantity available at the best quote and, if the quantity they want to trade is higher,

they place, for the residual quantity, a limit order at a price such that their order

will be first in the queue of orders written in the book2. We create heterogeneity

assuming that investors have imperfect information about the joint distribution of

returns. In particular, we allow agents to hold arbitrary priors about the univari-

ate marginal distribution of returns, and we make agents update those distribution

using past realized market prices. We concentrate our attention on analyzing theimpact of a learning process about the marginal distributions of returns assum-

ing that agents have a constant common view of the assets association structure.

They correctly apply a copula function to generate the joint distribution of returns

to be used to determine the optimal portfolio allocations. We assign to all agents

the same investment horizon, but we create asynchronous updating implicitly as-

suming that different agents (or groups of agents) entered the market at different

moments in time. Finally, we assume that investors are myopic in the sense that,

at the beginning of the investment horizon they choose their portfolios as if there

will be no further trading. At the end of the investment horizon agents use the

observed market prices to update the joint distribution of returns and choose theirnew optimal portfolio3. In this way we simplify the optimization problem making

investors demand functions dependent on time only through the learning process.

In Consiglio and Russino (2005) we used the same setting and we assigned

to the investors a prospect-type utility function (Kahneman and Tversky, 1979).

We have shown that, under learning, the automated auction system generates ir-

regular price series characterized by sharp increases and decreases (looking like

bubbles and crashes), but that the jumps in the price series are not related to sudden

changes in the optimal portfolio weights. We analyzed the unconditional distrib-

ution of price changes and we provided evidence supporting the hypothesis that

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In an automated financial market, trading occurs through an electronic order book withoutinvolving financial intermediaries. In this market setting, agents have two types of choices to

make: first, they have to decide the sign and the size of the order; second, they have to choose

what type of order to submit (limit or market order). In this paper we concentrate our attention

on the interactions between the endogenous order flow, driven by the evolution of the optimal

target portfolio allocations, and the price dynamics, imposing exogenously a common order type

submission strategy to all agents. See Consiglio et al. (2005) for an analysis of the effect of

allowing the agents to choose the type of order to submit on the basis of the information about

market conditions revealed by the state of the book, in a setting with exogenously assigned target

allocations.3See Consiglio and Russino (2005) for the details of the model that we implement.

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the parameters characterizing the learning process affect significantly the evolu-

tion of market liquidity, and that the variability of market liquidity determines theobserved bubble-like phenomena.

This paper is an extension of Consiglio and Russino (2005) in two directions.

First, we analyze what is the role played by the assumed portfolio optimization

model in affecting the market dynamics. That is, maintaining constant all the

parameters governing the learning process, we compare two settings where we

change the utility function assigned to the agents. In the first setting, we use, as

in Consiglio and Russino (2005), a prospect-type utility function. In particular,

we assume that each investor has an initial level of wealth and a target growth

rate to reach within his investment horizon. The investor must determine an asset

allocation strategy so that the portfolio growth rate will be sufficient to reach thetarget. We model the utility function in terms of deviations, measured at regular

intervals, from a specified target, and we assume that investors are more sensi-

tive to downside movements. In the second setting, we assign to the investors a

standard mean-variance reduced utility function and we study the differences that

emerge.

Second, we study how the time-series behavior of price changes, market liq-

uidity, and trading activity is affected by the learning process. We use the high-

frequency data relative to the order flow and the structure of the book to analyze

the short-run impact of those variables on price changes. Following Engle and

Patton (2004), we estimate a VAR model for the bid and ask price changes andwe include as regressors variables representing the characteristics of the orders

arriving in the market and the structure of the book.

References

Barberis, N.: 2000, Investing for the Long Run when Returns are Predictable,

Journal of Finance 55, 225264.

Bossaerts, P.: 1999, LearningInduced Securities Price Volatility, Working Paper,

California Institute of Technology.

Brennan, M. and Y., X.: 2001, Stock Price Volatility and Equity Premium, Journal

of Monetary Economics 47, 249283.

Consiglio, A., Lacagnina, V. and Russino, A.: 2005, A simulation analysis of the

microstructure of an order driven financial market with multiple securities and

portfolio choices, Quantitative Finance 5(1), 7187.

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Consiglio, A. and Russino, A.: 2005, How Does Learning Affect Market Liquid-

ity? A Simulation Analysis of a Double-Auction Financial Market with Portfo-lio Traders, http://ssrn.com/abstract=876415.

Engle, R. F. and Patton, J.: 2004, Impacts of Trades in an Error-Correction Model

of Quote Prices, Journal of Financial Markets 7, 125.

Guidolin, M. and Timmermann, A.: 2005, Properties of Asset Prices Under Al-

ternative Learning Schemes, Working Paper 009, Federal Reserve Bank of St.

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Hommes, C. H.: 2005, Heterogeneous Agent Models in Economics and Finance,

in K. L. Judd and L. Tesfatsion (eds), Handbook of Computational Economics,Vol. 2, Elsevier Science.

Kahneman, K. and Tversky, A.: 1979, Prospec Theory: an Analisys of Decision

under Risk, Econometrica 47(2), 263291.

Lewellen, J. and Shanken, J.: 2002, Learning, Asset-Pricing Tests, and Market

Efficiency, The Journal of Finance LVII, 11131145.

Y., X.: 2001, Learning about Predictability: The Effect of Parameter Uncertainty

on Dynamic Asset Allocation, The Journal of Finance 56, 205246.

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dyamics of quote prices in artificial mkts

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