Paper: arXiv 2311.15635

Abstract

This study evaluates the practical usefulness of continuous-time arbitrage strategies designed to exploit serial correlation in fractional financial markets. Specifically, we revisit the strategies of Shiryaev (1998) and Salopek (1998) and transfer them to a real-world setting by distretizing their dynamics and introducing transaction costs. In Monte Carlo simulations with various market and trading parameter settings as well as a formal analysis of discretization error, we show that both are promising with respect to terminal portfolio values and loss probabilities. These features and complementary sparsity make them worth serious consideration in the toolkit of quantitative investors.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper is mathematically dense, featuring advanced stochastic calculus (fBm SDEs, Riemann-Stieltjes integrals) and rigorous discretization error analysis, warranting a high math score. However, it lacks real-world data application, relying instead on Monte Carlo simulations with parameter sweeps and sensitivity checks, which is moderately rigorous but falls short of live backtesting, justifying a mid-range empirical score.

Research Flowchart

  flowchart TD
  A["Research Goal: Assess practicality of continuous-time arbitrage strategies for fractional markets with transaction costs"] --> B["Key Methodology: Discretization & Simulation"]
  B --> C["Computational Process: Monte Carlo simulations with various market/trading parameters"]
  C --> D["Computational Process: Formal analysis of discretization error"]
  D --> E["Key Findings: Both strategies are promising regarding terminal values & loss probabilities"]
  E --> F["Outcome: Suggested as viable tools for quantitative investors"]