iCOS: Option-Implied COS Method

ArXiv ID: 2309.00943 “View on arXiv”

Authors: Unknown

Abstract

This paper proposes the option-implied Fourier-cosine method, iCOS, for non-parametric estimation of risk-neutral densities, option prices, and option sensitivities. The iCOS method leverages the Fourier-based COS technique, proposed by Fang and Oosterlee (2008), by utilizing the option-implied cosine series coefficients. Notably, this procedure does not rely on any model assumptions about the underlying asset price dynamics, it is fully non-parametric, and it does not involve any numerical optimization. These features make it rather general and computationally appealing. Furthermore, we derive the asymptotic properties of the proposed non-parametric estimators and study their finite-sample behavior in Monte Carlo simulations. Our empirical analysis using S&P 500 index options and Amazon equity options illustrates the effectiveness of the iCOS method in extracting valuable information from option prices under different market conditions. Additionally, we apply our methodology to dissect and quantify observation and discretization errors in the VIX index.

Keywords: Fourier-cosine method (iCOS), risk-neutral densities, non-parametric estimation, option pricing, VIX index, Derivatives (Options)

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematical tools including Fourier-cosine series, characteristic functions, and asymptotic theory with derivations, indicating high mathematical complexity. It also demonstrates strong empirical rigor with extensive Monte Carlo simulations, real-world data applications (S&P 500, Amazon, VIX), and explicit discussion of estimation errors, making it backtest-ready.
  flowchart TD
    A["Research Goal: Non-parametric Estimation of RND & Option Pricing"] --> B["Input: Observed Market Option Prices"]
    B --> C["Methodology: iCOS Framework"]
    C --> D["Step 1: Estimate Option-Implied<br>COS Coefficients"]
    C --> E["Step 2: Reconstruct Risk-Neutral<br>Density via Inverse COS Transform"]
    D & E --> F{"Computational Process"}
    F --> G["Compute Option Prices &amp; Sensitivities<br>Extract VIX Information"]
    G --> H["Key Findings &amp; Outcomes"]
    H --> I["Model-Free, Non-Parametric Estimation"]
    H --> J["Proven Accuracy via<br>Monte Carlo &amp; S&amp;P 500/Amazon Data"]
    H --> K["Quantification of<br>Observation &amp; Discretization Errors"]