Paper: arXiv 2303.16371

Authors: Gurdip Bakshi, John Crosby, Xiaohui Gao

Abstract

Emphasizing the statistics of jumps crossing the strike and local time, we develop a decomposition of equity option risk premiums. Operationalizing this theoretical treatment, we equip the pricing kernel process with unspanned risks, embed (unspanned) jump risks, and allow equity return volatility to contain unspanned risks. Unspanned risks are consistent with negative risk premiums for jumps crossing the strike and local time and imply negative risk premiums for out-of-the-money call options and straddles. The empirical evidence from weekly and farther-dated index options is supportive of our theory of economically relevant unspanned risks and reveals ``dark matter" in option risk premiums.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a rigorous theoretical framework decomposing option risk premiums via local time and jump risks crossing the strike, incorporating unspanned risks into the pricing kernel process. The empirical testing on weekly and longer-dated index options provides strong validation for the theoretical ‘dark matter’ premium components, combining high mathematical rigor with solid empirical execution.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain Equity Option Risk Premiums & Unspanned Risks] --> B[Data: Index Options Data - Weekly & Farther-Dated]
    B --> C[Methodology: Theoretical Decomposition of Option Risk Premiums]
    C --> D[Model Setup: Equip Pricing Kernel with Unspanned & Jump Risks]
    D --> E[Analysis: Evaluate Jumps Crossing Strike & Local Time Statistics]
    E --> F[Findings: Negative Risk Premiums for OTM Calls, Straddles & Jump/Local Time]
    F --> G[Outcome: Evidence of Economically Relevant 'Dark Matter' in Volatility]