Paper: arXiv 2601.17248

Authors: Desen Guo, Dan Pirjol, Xiaoyu Wang, Lingjiong Zhu

Abstract

We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. The leading-order asymptotics are obtained in closed-form. We apply our results to three examples: the Eraker model, a Kou-type model, and a folded normal model. Numerical illustrations are provided for these three examples that show the accuracy of predictions based on the asymptotic results.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper demonstrates strong theoretical math complexity by establishing analytical short-maturity asymptotics for VIX and European options under local-stochastic volatility models with compound Poisson jumps. However, its empirical rigor is primarily focused on numerical verification/simulations rather than backtesting against actual historical option market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Short-Maturity Asymptotics for VIX & European Options with Jumps] --> B[Model Framework: Local-Stochastic Volatility + Compound Poisson Jumps]
    B --> C[Derive Closed-Form Asymptotics: ATM & OTM Regimes]
    C --> D[Apply to Examples: Eraker, Kou-type, & Folded Normal Models]
    D --> E[Numerical Testing: Compare Asymptotic Predictions vs. Exact Prices]
    E --> F[Outcome: Accurate Lead-Order Option Pricing Formulae in Short-Maturity Regime]

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1 of 91 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.