zbMATH — the first resource for mathematics

Price equations with symmetric supply/demand; implications for fat tails. (English) Zbl 1409.91111
Summary: Implementing a set of microeconomic criteria, we develop price dynamics equations using a function of demand/supply with key symmetry properties. The function of demand/supply can be linear or nonlinear. The type of function determines the nature of the tail of the distribution based on the randomness in the supply and demand. For example, if supply and demand are normally distributed, and the function is assumed to be linear, then the density of relative price change has behavior $$x^{-2}$$ for large $$x$$ (i.e., large deviations). The exponent approaches $$-1$$ if the function of supply and demand involves a large exponent. The falloff is exponential, i.e., $$e^{-x}$$, if the function of supply and demand is logarithmic.
MSC:
 91B24 Microeconomic theory (price theory and economic markets)
zoverw
Full Text:
References:
 [1] Bachelier, L., Théorie de la spéculation, Ann. Sci. Éc. Norm. Super., 17, 21-86, (1900) · JFM 31.0241.02 [2] Black, F.; Scholes, M., The pricing of options and corporate liabilities, J. Political Econ., 81, 637-654, (1973) · Zbl 1092.91524 [3] Caginalp, G.; Balevonich, D., Asset flow and momentum: Deterministic and stochastic equations, Phil. Trans. Royal Soc. A, 357, (1999), 2119-2113 · Zbl 0935.91011 [4] Caginalp, C.; Caginalp, G., The quotient of normal random variables and application to asset price fat tails, Physica A, 499, 457-471, (2018) [5] Champagnat, N.; Deaconu, M.; Lejay, A.; Navet, N.; Boukherouaa, S., An Empirical Analysis of Heavy-Tails Behavior of Financial Data: The Case for Power Laws, (2013), HAL archives-ouvertes [6] Dacorogna, M., Pictet, O., 1997. Heavy tails in high-frequency financial data. Available at SSRN: https://ssrn.com/abstract=939. [7] Daníelsson, J.; Jorgensen, B. N.; Samorodnitsky, G.; Sarma, M.; de Vries, C. G., Fat tails, VaR and subadditivity, J. Econometrics, 172, 283-291, (2013) · Zbl 1443.62343 [8] Díaz-Francés, E.; Rubio, F. J., On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables, Statist. Papers, 1-15, (2013) [9] Fama, E., The Behavior of Stock-Market Prices, J. Bus., 38, 34-105, (1965) [10] Gabaix, X.; Gopikrishnan, P.; Plerou, V.; Stanley, H. E., Institutional investors and stock market volatility, Q. J. Econ., 121, 461-504, (2006) · Zbl 1179.91265 [11] Henderson, J.; Quandt, R., Microeconomic Theory - A Mathematical Approach, (1980), McGraw-Hill: McGraw-Hill New York [12] Hirshleifer, J.; Glazer, A.; Hirshleifer, D., Price Theory and Applications: Decisions, Markets, and Information, (2005), Cambridge Univ. Press [13] Kemp, M., Extreme Events - Robust Portfolio Construction in the Presence of Fat Tails, (2011), Wiley Finance: Wiley Finance Hoboken, NJ [14] Kirchler, M.; Huber, J., Fat tails and volatility clustering in experimental asset markets, J. Econom. Dynam. Control, 31, 1844-1874, (2007) · Zbl 1201.91230 [15] Mandelbrot, B., Sur certain prix speculatifs: faits empirique et modele base sur les processes stables additifs de Paul Levy, C. R. Acad. Sci., 254, 3968-3970, (1962) · Zbl 0100.34904 [16] Mandelbrot, B.; Hudson, R., The Misbehavior of Markets: A Fractal View of Financial Turbulence, (2007), Basic Books: Basic Books New York [17] Marsaglia, G., Ratios of normal variables, J. Stat. Softw., 16, 1-10, (2006) [18] Merdan, H.; Alisen, M., A mathematical model for asset pricing, App. Math. Comp., 218, 1449-1456, (2011) · Zbl 1237.91105 [19] Plott, C., Pogorelskiy, K., 2016. Call market experiments: efficiency and price discovery through multiple calls and emergent Newton adjustments. Available at SSRN: https://ssrn.com/abstract=2602034 or http://dx.doi.org/10.2139/ssrn.2602034. [20] Schneeweiss, C., On a formalisation of the process of quantitative model building, Eur. J. Oper. Res., 29, 24-41, (1987) [21] Taleb, N., Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, (2005), Random House: Random House New York [22] Taleb, N., Daniel, G., 2011. The problem is beyond psychology: The real world is more random than regression analyses. http://ssrn.com/abstract=1941792. [23] Tong, Y., The Multivariate Normal Distribution, (1990), Springer-Verlag: Springer-Verlag New York · Zbl 0689.62036 [24] Watson, D.; Getz, M., Price Theory and Its Uses, (1981), University Press of America: University Press of America Lanham, MD [25] Wilmott, P., Paul Wilmott on Quantitative Finance, (2013), John Wiley & Sons · Zbl 1127.91002 [26] Xavier, G., Power laws in economics and finance, Annu. Rev. Econ., 1, 255-294, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.