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

Davide Lauria, W. Brent Lindquist (), Svetlozar T. Rachev and Yuan Hu
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Davide Lauria: Department of Economics, Statistics & Finance, University of Calabria, 87036 Calabria, 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

JRFM, 2025, vol. 18, issue 5, 1-43

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.

Keywords: binary trees; asset pricing; option pricing; market microstructure; technical analysis (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2025
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