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Modeling Of Stock Returns In Continuous Vis-À-Vis Discrete Time Is Equivalent, Respectively, To The Conditioning Of Stock Returns On A Random Walk Process For Trade Imbalances Vis-À-Vis A Random Walk Process For Evolution Of Information

Author

Listed:
  • OGHENOVO A. OBRIMAH

    (Department of Business, FISK University, 1000 17th Avenue N., Nashville TN 37208, USA)

  • WING-KEUNG WONG

    (Department of Finance, Fintech Center, and Big Data Research Center, Asia University, Taichung, Taiwan3Department of Medical Research, China Medical University Hospital, Taichung, Taiwan4Department of Economics and Finance, Hang Seng University of Hong Kong, Hong Kong, China)

Abstract

Let p, p(I), ϱ and p(M) denote, respectively, the current stock price, the future stock price that is conditioned on information, the minimum stock market tick size and the realized future stock price. Formal theoretical proofs in this study show modeling of stock returns in continuous time induces stock returns that have parameterization as gambles over lotteries. Stock returns have parameterization as gambles because in the presence of fairness of formation of p<[p+ϱ]pt(I)>[pt+ϱ], because all else constant, an inversion of the perturbing conditionally positive trade imbalance induces pt+1(M)pt(I) that is statistic for risk; risk, as such is well parameterized, that is, does not coincide with its materialization (note that whereas volatility is statistic for risk, it is not a statistic for materialization of risk; a statistic for risk necessarily is robust to non-materialization of risk). Given modeling in continuous time does not facilitate either of the two sufficiency conditions, always, risk has parameterization as the probability that pt+1(M)

Suggested Citation

  • Oghenovo A. Obrimah & Wing-Keung Wong, 2022. "Modeling Of Stock Returns In Continuous Vis-À-Vis Discrete Time Is Equivalent, Respectively, To The Conditioning Of Stock Returns On A Random Walk Process For Trade Imbalances Vis-À-Vis A Random Wal," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-35, June.
    • Handle: RePEc:wsi:afexxx:v:17:y:2022:i:02:n:s2010495222500105
    DOI: 10.1142/S2010495222500105
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    Cited by:

    1. Moawia Alghalith & Wing-Keung Wong, 2022. "Option Pricing Under an Abnormal Economy: using the Square Root of the Brownian Motion," Advances in Decision Sciences, Asia University, Taiwan, vol. 26(Special), pages 4-18, December.

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