Paper: arXiv 2304.02356

Authors: Davide Lauria, W. Brent Lindquist, Svetlozar T. Rachev, Yuan Hu

Abstract

We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include moving average or autoregressive behavior. Our model is market-complete, arbitrage-free, and preserves all of the parameters governing the historical (natural world) price dynamics when passing to an equivalent martingale (risk-neutral) measure. Specifically, this includes the instantaneous mean and variance of the asset return and the instantaneous probabilities for the direction of asset price movement. We believe this is the first paper to demonstrate the ability to include market microstructure effects in dynamic asset/option pricing in a market-complete, no-arbitrage, format.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a novel theoretical framework unifying market microstructure history-dependence (like MA/AR processes) with complete-market, arbitrage-free option pricing using discrete trees. While mathematically innovative and foundational for dynamic asset pricing, the provided abstract and excerpt lack empirical backtesting, real-world data validation, or calibration against market options.

Research Flowchart

  flowchart TD
    A[Research Goal: Incorporate Market Microstructure<br>into Dynamic Option Pricing] --> B[Input Parameters: Natural World Asset Dynamics<br>Mean, Variance & Path Dependence]
    B --> C[Construct History-Dependent Discrete Binary Tree<br>Models MA/AR Microstructure Effects]
    C --> D[Pass to Equivalent Martingale Measure<br>Risk-Neutral Pricing Transformation]
    D --> E[Outcome: Arbitrage-Free, Market-Complete Framework<br>Preserves Microstructure Parameters]