Option Pricing for the Variance Gamma Model: A New Perspective

Paper: arXiv 2306.10659

Authors: Yuanda Chen, Zailei Cheng, Haixu Wang

Abstract

The variance gamma model is a widely popular model for option pricing in both academia and industry. In this paper, we provide a new perspective for pricing European style options for the variance gamma model by deriving closed-form formulas combining the randomization method and fractional derivatives. We also compare our results with various existing results in the literature by numerical examples.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically sophisticated analytical approach for European option pricing under the Variance Gamma model using fractional derivatives and randomization. While strong on theoretical innovation and formula derivation, the empirical validation is limited to basic numerical examples rather than extensive real-world market backtests.

Research Flowchart

  flowchart TD
    A[Research Goal: Derive Closed-Form Formulas for Pricing European Options under Variance Gamma Model] --> B[Inputs: VG Model Parameters & European Option Contracts]
    B --> C[Methodology: Combine Randomization Method & Fractional Derivatives]
    C --> D[Computational Process: Derive New Mathematical Closed-Form Formulas]
    D --> E[Numerical Analysis: Compare New Formulas against Existing Literature Methods]
    E --> F[Outcomes: Validated Efficient Closed-Form Option Pricing Perspective]