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Dynamics of asset price changes: Statistical and differential equations models

DeSantis, Mark (2011) Dynamics of asset price changes: Statistical and differential equations models. Doctoral Dissertation, University of Pittsburgh.

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    Abstract

    This dissertation is comprised of two related tracts: (i) Quantitative Modeling and (ii) Analysis of Asset Flow Differential Equations. In the former a data set of over 100,000 daily closed-end fund prices is analyzed using mixed-effects regressions with the objective of understanding price dynamics. This analysis provides strong statistical evidence that relative daily price change is positively influenced by valuation, recent price trend, short term volatility, volume trend, and the M2 money supply. There is a strong nonlinearity in the influence of the price trend, so that a significantly large recent uptrend has a negative influence on the subsequent day's relative price change. The nonlinearity is the key to an understanding of the competing role of price trend, since a single large data set exhibits both under- and overreaction in different regimes of the independent variables. The role of long term volatility is not a clear-cut risk/return inverse relation; rather there is an ambiguous and complicated relationship between volatility and return. Standardization of the independent regression variables allows for a more direct comparison of each factor's influence on the return.In the latter a two-group asset flow model of a financial instrument with one group focused on price trend, the other on value, is considered. The existence of both stable and unstable regions for the system of differential equations is proven. It is shown that a strong motivation based on (recent) price trend is associated with instability. Numerical computations using a set of typical parameters describe regions of stability and instability. A precise limiting connection between the discrete and differential equations is also established.


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    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmail
    Committee ChairCaginalp, Gunduzcaginalp@pitt.edu
    Committee MemberSwigon, Davidswigon@pitt.edu
    Committee MemberIyengar, Satishssi@pitt.edu
    Committee MemberTroy, Williamtroy@math.pitt.edu
    Title: Dynamics of asset price changes: Statistical and differential equations models
    Status: Unpublished
    Abstract: This dissertation is comprised of two related tracts: (i) Quantitative Modeling and (ii) Analysis of Asset Flow Differential Equations. In the former a data set of over 100,000 daily closed-end fund prices is analyzed using mixed-effects regressions with the objective of understanding price dynamics. This analysis provides strong statistical evidence that relative daily price change is positively influenced by valuation, recent price trend, short term volatility, volume trend, and the M2 money supply. There is a strong nonlinearity in the influence of the price trend, so that a significantly large recent uptrend has a negative influence on the subsequent day's relative price change. The nonlinearity is the key to an understanding of the competing role of price trend, since a single large data set exhibits both under- and overreaction in different regimes of the independent variables. The role of long term volatility is not a clear-cut risk/return inverse relation; rather there is an ambiguous and complicated relationship between volatility and return. Standardization of the independent regression variables allows for a more direct comparison of each factor's influence on the return.In the latter a two-group asset flow model of a financial instrument with one group focused on price trend, the other on value, is considered. The existence of both stable and unstable regions for the system of differential equations is proven. It is shown that a strong motivation based on (recent) price trend is associated with instability. Numerical computations using a set of typical parameters describe regions of stability and instability. A precise limiting connection between the discrete and differential equations is also established.
    Date: 21 July 2011
    Date Type: Completion
    Defense Date: 20 April 2011
    Approval Date: 21 July 2011
    Submission Date: 21 April 2011
    Access Restriction: No restriction; The work is available for access worldwide immediately.
    Patent pending: No
    Number of Pages: 147
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-04212011-154440
    Uncontrolled Keywords: Mathematical Finance
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:40
    Last Modified: 10 Jul 2013 14:55
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-04212011-154440/, etd-04212011-154440

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