Term Structures, Shape Constraints, and Inference for Option Portfolios

Abstract

The illiquidity of options at long horizons has made it dicult to study the long-run properties of several key option portfolios, including the volatility index (VIX) and related measures. This paper proposes a new nonparametric framework to aid in the estimation of option portfolios at arbitrary maturities (even sparsely traded ones) and develops an asymptotic distribution theory for those portfolios. The distribution theory is used to quantify the estimation error induced by computing integrated option portfolios from a finite sample of noisy option data. Moreover, by relying on the method of sieves, the framework is nonparametric, adheres to economic shape restrictions for arbitrary maturities, yields closed-form option prices, and is easy to compute. The framework also permits the extraction of the entire term structure of risk-neutral distributions in closed-form. Monte Carlo simulations confirm the framework’s performance in finite samples. An application to the term structure of the synthetic variance swap portfolio finds sizeable uncertainty around the swap’s true fair value, particularly when the variance swap is synthesized from noisy long-maturity options. A nonparametric investigation into the term structure of the variance risk premium finds growing compensation for variance risk at long maturities.