Franke, Reiner (2007) A prototype model of speculative dynamics with position-based trading. Working Paper. Warwick Business School, Financial Econometrics Research Centre, Coventry.

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Abstract

To avoid the indeterminate and generally unbounded positions of the agents in financial market models with order-based trading, the paper considers the alternative of position-based strategies. To this end it extracts a prototype model from the literature, with fundamentalists, chartists, and a risk-averse market maker. The deterministic formulation of the model leads to a neutral delay differential equation of the price, whose mathematical analysis is non-standard. The stability conditions are nevertheless quite analogous to the order-based Beja–Goldman model. The effects of parameter variations are also studied in a stochastic setting, where special emphasis is put on the misalignment between price and the time-varying fundamental value, and on the differential profits of fundamentalists and chartists.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre Faculty of Social Sciences > Warwick Business School
Library of Congress Subject Headings (LCSH):	Assets (Accounting), Fundamental groups (Mathematics), Price -- Mathematical models, Equilibrium (Economics), Delay differential equations
Series Name:	Working papers (Warwick Business School. Financial Econometrics Research Centre)
Publisher:	Warwick Business School, Financial Econometrics Research Centre
Place of Publication:	Coventry
Date:	December 2007
Number:	No.07-
Number of Pages:	56
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Sixth Framework Programme (European Commission) (FP6)
Grant number:	516446 (SFP)
References:	Arnold, L. (1998), Random Dynamical Systems. New York: Springer. Barker, K. and Whitesides, J.L. (1976), “Stability of neutral equations with constant time delays”, NASA Langley Research Center (http://ntrs.nasa.gov./archive/nasa/casi.ntrs.nasa.gov/19770003358 1977003358.pdf). Beja, A. and Goldman, M.B. (1980), “On the dynamic behavior of prices in disequilibrium”, Journal of Finance, 35, 235–248. B¨ohm, V. and Chiarella, C. (2005), “Mean variance preferences, expectations formation, and the dynamics of random asset prices”, Mathematical Finance, 15, 61–97. Bradfield, J. (1979), “A formal dynamic model of market making”, Journal of Financial and Quantitative Analysis, 14, 275–291. Carvalho, R. (2001), “The dynamics of the linear random Farmer model”, Instituto Superior Técnico, Lisboa, and University College, London (arXiv:cond-mat/0107150v1). Day, R.D. (1997), “Complex dynamics, market mediation and stock price behavior”, North American Actuarial Journal, 1:3, 6–23. Farmer, J.D. (2001), “Toward agent-based models for investment”, in Developments in Quantitative Investment Models, AIMR (www.santafe.edu/~jdf/papers/aimr.pdf). Farmer, J.D. and Joshi, S. (2002), “The price dynamics of common trading strategies”, Journal of Economic Behavior and Organization, 49, 149–171. Forde, J. and Nelson, P. (2004), “Applications of Sturm sequences to bifurcation analysis of delay differential equation models”, Journal of Mathematical Analysis and Applications, 300, 273–284. Futia, C.A. (1982), “Invariant distributions and the limiting behavior of Markovian economic models”, Econometrica, 50, 377–408. Gandolfo, G. (1997), Economic Dynamics. Berlin: Springer. Goodwin, R.M. (1951), “The non-linear accelerator and the persistence of business cycles”, Econometrica, 19, 1–17. Han, Q.-L. (2001), “On delay-dependent stability for neutral delay-differential systems”, International Journal of Applied Mathematics and Computer Science, 11, 965–976. He, X.-Z. and Li, Y. (2007), “Power-law behaviour, heterogeneity, and trend chasing”, Journal of Economic Dynamics and Control, 31, 3396–3426. Hu, G.-D. and Hu, G.-D. (1996), “Some simple criteria for stability of neutral delaydifferential systems”, Applied Mathematics and Computation, 80, 257–271. Kalecki, M. (1935), “A theory of the business cycle”, Econometrica, 3, 327–344. Markowitz, H. (1959), Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley & Sons. Pape, B. (2007), Asset Allocation, Multivariate Position Based Trading, and the Stylized Facts, Doct. Thesis, University of Vaasa. Schenk–Hopp´e, K.R. and Schmalfuß, B. (2001), “Random fixed points in a stochastic Solow growth model”, Journal of Mathematical Economics, 36, 19–30. Sethi, R. (1996), “Endogenous regime switching in financial markets”, Structural Change and Economic Dynamics, 7, 99–118. Westerhoff, F.H. (2003), “Market-maker, inventory control and foreign exchange dynamics”, Quantitative Finance, 3, 363–369.
URI:	http://wrap.warwick.ac.uk/id/eprint/1735

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