Paper: arXiv 2504.06942

Authors: Yan-Feng Wu, Jian-Qiang Hu

Abstract

We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form density approximations (up to a normalization constant) via moment matching for both conditional and unconditional distributions. Our framework enables important financial applications, including efficient option pricing and exact simulation for affine jump diffusions. Numerical experiments demonstrate the method’s superior computational efficiency compared to existing simulation techniques, while preserving numerical precision.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a mathematically rigorous recursive framework for explicit, closed-form moment derivations of Affine Jump Diffusions. It leverages these moments to construct Pearson family density approximations, offering substantial computational speedups for simulation and option pricing without reliance on Bessel function evaluations.

Research Flowchart

  flowchart TD
    A["Research Goal: Fast & accurate density approximation for Affine Jump Diffusions (AJDs)"] --> B["Input: AJD Model Specifications (State-independent jump intensities)"]
    B --> C["Methodology: Derivation of recursive closed-form conditional & unconditional moments"]
    C --> D["Computational Process: Construct density via closed-form moment matching"]
    D --> E["Applications: Efficient option pricing & exact simulation"]
    E --> F["Outcomes: Superior computational efficiency over standard simulation while preserving precision"]

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1 of 103 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.