Path weighting sensitivities

ArXiv ID: 2411.13403 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to address the large variance happening when the first simulation time step is small. We also propose a covariance inflation technique to addresses the degenerator case when the covariance matrix is singular. The stock dynamics we consider is given in a general functional form, which includes the classical Black-Scholes model, the implied distribution model, and the local volatility model.

Keywords: sensitivities (Greeks), path weighting, variance reduction, path-dependent derivatives, local volatility model, Derivatives

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, deriving explicit path weighting formulas and variance reduction techniques for greeks calculation, with heavy reliance on stochastic calculus and matrix algebra. While it mentions open-source code availability and numerical tests, the primary focus is on theoretical derivations and asymptotic analysis rather than extensive empirical backtesting or implementation-heavy validation.

  flowchart TD
    A["Research Goal: Compute Path-Dependent Greeks via Path Weighting"] --> B{"Stock Dynamics Input<br/>(e.g., Black-Scholes, Local Vol)"}
    B --> C["Key Methodology: Explicit Path Weighting Formulas"]
    C --> D{"Computational Process"}
    D --> E["Variance Reduction Adjustment<br/>(Addressing small time steps)"]
    D --> F["Covariance Inflation Technique<br/>(Handling singular covariance)"]
    E & F --> G["Final Computation of Sensitivities"]
    G --> H["Key Outcomes:<br/>1. Efficient Greeks Calculation<br/>2. Reduced Variance & Numerical Stability"]