Asset price volatility and price extrema

Carey Caginalp; Gunduz Caginalp

doi:10.3934/dcdsb.2020010

Article Contents

2020, Volume 25, Issue 5: 1935-1958. Doi: 10.3934/dcdsb.2020010

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Asset price volatility and price extrema

Carey Caginalp^1,2, and
Gunduz Caginalp^2,

1.
Economic Science Institute, Chapman Unviersity, Orange, CA 92866
2.
Mathematics Department, University of Pittsburgh, Pittsburgh, PA 15260

Received: February 2019

Revised: June 2019

Early access: December 2019

Published: May 2020

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Abstract

The relationship between price volatility and expected price market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the supply and demand, rather than assuming that price has randomness on an empirical basis. Within a general setting of changing fundamentals, the volatility is maximum when expected prices are changing most rapidly, with the maximum of volatility reached prior to the maximum of expected price. A key issue is that randomness arises from the supply and demand, and the variance in the stochastic differential equation governing the logarithm of price must reflect this. Analogous results are obtained by further assuming that the supply and demand are dependent on the deviation from fundamental value of the asset.

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Mathematics Subject Classification: 91B25, 91B70, 91G80.

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