Pricing ultra-short-term volatility surfaces

Abstract

Options with maturities below one week, hereafter ultra-short-term options, have seen a sharp increase in trading activity in recent years. Yet, these instruments are difficult to price jointly using classical pricing models due to the pronounced oscillations observed in the at-the-money implied-volatility term structure across ultra-short-term tenors. We propose Edgeworth++, a parsimonious jump–diffusion model featuring a nonparametric stochastic volatility component, which provides flexibility in capturing implied-volatility smiles for each tenor, combined with a deterministic shift extension, which allows the model to fit rich at-the-money implied-volatility shapes across tenors. A local (in tenor) expansion of the process characteristic function suited to price ultra-short tenor options is derived and pricing is conducted in closed form. We discuss the benefits of the proposed approach relative to benchmarks.