Derivation of non-classical stochastic price dynamics equations

Physica A 560, 15 December 2020, 125118

29 Pages Posted: 2 Aug 2019 Last revised: 22 Jan 2021

See all articles by Carey Caginalp

Carey Caginalp

University of Pittsburgh; Chapman University

Gunduz Caginalp

University of Pittsburgh - Department of Mathematics

Date Written: August 1, 2019

Abstract

We analyze the relative price change of assets starting from basic supply/demand considerations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. The variance in the relative price change is then dependent on the supply and demand, and is closely connected to the expected return. An important consequence for risk assessment and options pricing is the implication that variance is highest when the magnitude of price change is greatest, and lowest near market extrema. This differs from the standard equation in mathematical finance in which the expected return and variance are decoupled. The methodology has implications for the basic framework for risk assessment, suggesting that volatility should be measured in the context of regimes of price change. The model we propose shows how investors are often misled by the apparent calm of markets near a market peak. Risk assessment methods utilizing volatility can be improved using this formulation.

Keywords: asset prices, stochastic models, price variance, volatility

JEL Classification: C00, G12, G40

Suggested Citation

Caginalp, Carey and Caginalp, Gunduz, Derivation of non-classical stochastic price dynamics equations (August 1, 2019). Physica A 560, 15 December 2020, 125118, Available at SSRN: https://ssrn.com/abstract=3430867 or http://dx.doi.org/10.2139/ssrn.3430867

Carey Caginalp

University of Pittsburgh

Pittsburgh, PA 15260
United States

Chapman University ( email )

One University Dr.
Orange, CA 92866
United States

Gunduz Caginalp (Contact Author)

University of Pittsburgh - Department of Mathematics ( email )

507 Thackeray Hall
Pittsburgh, PA 15260
United States
412-624-8339 (Phone)
412-624-8397 (Fax)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
27
Abstract Views
299
PlumX Metrics