Quantifying stock-price response to demand fluctuations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 2, 2002, Pages

  Plerou, Vasiliki ^a   Gopikrishnan, Parameswaran ^a   Gabaix, Xavier ^b   Stanley, H Eugene ^a  

^a Boston University   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEMAND FLUCTUATIONS; SPIN SYSTEMS; STANDARD DEVIATION; VOLUME IMBALANCES;

CORRELATION THEORY; FUNCTIONS; MAGNETIC FIELD EFFECTS; MAGNETIC SUSCEPTIBILITY; MAGNETIZATION; NATURAL FREQUENCIES; NONLINEAR SYSTEMS; PHASE TRANSITIONS;

MAGNETIC FIELDS;

EID: 37649027271     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.027104     Document Type: Article

References (26)

1. Y.-C. Zhang, Physica A 269, 30 (1999) presents an argument for a square-root relationship between price changes and demand.
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4. The Trades and Quotes Database (New York Stock Exchange, New York, 1994–95).
5. Following the procedure of C.M. Lee and M.J. Ready, J. Financ. 46, 733 (1991), we use the prevailing quote at least 5 s prior to the trade. Lee and Ready report that (Formula presented) of the quotes are recorded prior to trade. They find that using the prevailing quote at least 5 s prior to the trade mitigates this problem.
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8. Trades occurring within the (Formula presented) and (Formula presented) or at the mid-quote (Formula presented) arise when a market buy and sell order occur simultaneously, or when the specialist or floor brokers with standing orders respond to a market order by bettering the quote. According to Lee and Ready 5 the latter is more often the case. In our case, an average of (Formula presented) of the trades remain indeterminate. See also L. Harris, J. Financ. Quant. Anal. 24, 29 (1989).
9. The motivation for considering the difference between the number of buyer- and seller-initiated trades is due to the finding that price changes when conditioned on the number of trades does not show significant dependence on volume per trade [C. Jones, G. Kaul, and M. Lipson, Rev. Financ. Stud. 7, 631 (1994)].
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15. A. Kempf and O. Korn, J. Financ. Markets 2, 29 (1999), also report a concave relationship between returns and volume imbalance.
16. To test that short-term anticorrelation in price changes (“bid-ask bounce”) do not affect the conditional expectation values, we have also used mid-quote changes and find similar results.
17. Regardless of the fitting function, the “flat” asymptotic behavior of (Formula presented) is consistent with what we expect from the distributions of G and (Formula presented). Since (Formula presented) has a distribution (Formula presented) with exponent (Formula presented) within the Lévy stable domain 10, the distribution (Formula presented) also has the same tail exponent, since the variables (Formula presented) and (Formula presented) in Eq. (2b) have only short-ranged time dependence. Price fluctuations have distribution (Formula presented) with (Formula presented) 20. Therefore, the asymptotic behavior of the function (Formula presented) must be bounded from above by (Formula presented), since for (Formula presented) with (Formula presented), the exponent (Formula presented) of (Formula presented) must be smaller than the empirical value of (Formula presented). Thus, for the consistency of tail exponents of G and (Formula presented), we must have (Formula presented) for large (Formula presented), which is consistent with the flat behavior of (Formula presented) for large (Formula presented) that we find. Zhang 1 presents an argument for (Formula presented).
18. Although we fit (Formula presented) with (Formula presented), there are alternative functions that fit (Formula presented) From Fig. 22(e), it is evident that (Formula presented) is weaker than any power of (Formula presented). In particular, we also obtain good fits using the function (Formula presented).
19. Y. Liu, Phys. Rev. E 60, 1390 (1999);M. Lundin et al., in Financial Markets Tick by Tick, edited by P. Lequeux (Wiley, New York, 1999), p. 91;
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