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Bridging Asset Pricing and Market Microstructure: Option Valuation in Roll’s Framework

Author

Listed:
  • Davide Lauria

    (Department of Economics, Statistics & Finance, University of Calabria, 87036 Calabria, Italy
    Current address: Department of Management, University of Bergamo, 24127 Bergamo, Italy.)

  • W. Brent Lindquist

    (Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Svetlozar T. Rachev

    (Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Yuan Hu

    (Independent Researcher, Rockville, MD 20852, USA)

Abstract

We introduce a binary tree for pricing contingent claims when the underlying security prices exhibit history dependence. We apply the model to the specific cases of moving-average and autoregressive behavior that are characteristic of price histories induced by market microstructure behavior. Our model is market-complete and arbitrage-free. When passing to the risk-neutral measure, the model preserves all parameters governing the natural-world price dynamics, including the instantaneous mean of the asset return and the instantaneous probabilities for the direction of asset price movement. This preservation holds for arbitrarily small, but non-zero, time increments characteristic of market microstructure transactions. In the (unrealistic) limit of continuous trading, the model reduces to continuous diffusion price processes, with the concomitant loss of the microstructure information.

Suggested Citation

  • Davide Lauria & W. Brent Lindquist & Svetlozar T. Rachev & Yuan Hu, 2025. "Bridging Asset Pricing and Market Microstructure: Option Valuation in Roll’s Framework," JRFM, MDPI, vol. 18(5), pages 1-43, April.
    • Handle: RePEc:gam:jjrfmx:v:18:y:2025:i:5:p:230-:d:1642131
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