Paper: arXiv 2304.06202

Authors: Karen Grigorian, Robert Jarrow

Abstract

This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete market. This unique EMM in the fictitious market is uplifted to the original economy using the notion of consistency. For pedagogical purposes, we begin with simple setups and progressively extend to models of increasing generality.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework utilizing filtration reduction and measure lifting for jump-diffusion models. However, it is purely theoretical with minimal empirical validation or backtesting methodology.

Research Flowchart

  flowchart TD
    A[Goal: Price & Hedge Derivatives in Incomplete Jump-Diffusion Markets] --> B[Inputs: Asset Price Dynamics & Jump-Diffusion Process]
    B --> C[Step 1: Apply Filtration Reduction to Fictitious Market]
    C --> D[Step 2: Derive Unique Equivalent Martingale Measure]
    D --> E[Step 3: Uplift Unique EMM to Original Economy via Consistency]
    E --> F[Outcome: Unique EMM & Consistent Pricing/Hedging Framework]