iCOS: Option-Implied COS Method

TL;DR

The paper introduces iCOS, a non-parametric Fourier-cosine based method for estimating risk-neutral densities and option sensitivities directly from market data without model assumptions, demonstrated through empirical analysis.

Contribution

It develops the first non-parametric, model-free Fourier-cosine method for option analysis, avoiding numerical optimization and providing theoretical and empirical validation.

Findings

Effective extraction of risk-neutral densities from options data.

Accurate quantification of observation and discretization errors in VIX.

Robust performance demonstrated on S&P 500 and Amazon options.

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.