Paper: arXiv 2510.14093

Authors: Rohan Shenoy, Peter Kempthorne

Abstract

This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation procedure through the absolute moments. We generalise the Laplace model to characterise the powerful variance gamma model of Madan et al. as a Gamma time-subordinated Brownian motion to price European call options via an Esscher transform method. We find that the Variance Gamma model is able to empirically explain excess kurtosis found in log-returns data, rejecting a Black-Scholes assumption in a hypothesis test.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a solid mathematical treatment of the Variance Gamma process, Laplace variance-mixtures, and Esscher transforms for option pricing. However, its novelty is limited as it largely synthesizes and reviews established literature (e.g., Madan et al.), and the empirical section is modest in scope.

Research Flowchart

  flowchart TD
    A[Goal: Model Stock Dynamics & Price Options via Variance-Gamma] --> B[Input: Log-Returns Data & European Call Options]
    B --> C[Volatility Estimation using Absolute Moments]
    C --> D[Subordinate Brownian Motion via Gamma Time-Process]
    D --> E[Price Options using Esscher Transform]
    E --> F[Findings: Captures Excess Kurtosis & Rejects Black-Scholes]

Cited References (36)

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  2. OPTION PRICING WITH V. G. MARTINGALE COMPONENTS (1991)
  3. Lévy Processes in Finance: Theory, Numerics, and Empirical Facts (2000)
  4. Pricing European Options under Stochastic Volatility Models: Case of Five-Parameter Variance-Gamma Process (2023)
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  8. Stochastic Volatility and Option Valuation: A Pricing-Density Approach (1995)
and 28 more
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  22. Option Pricing in a Dynamic Variance-Gamma Model (2010)
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  28. An Introduction to Harmonic Analysis (2004)

0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.