Ultra-short-term volatility surfaces

TL;DR

The paper introduces Edgeworth++, a jump-diffusion model with stochastic volatility and deterministic shifts, enabling fast, accurate pricing of ultra-short-term options with complex implied-volatility structures.

Contribution

It develops a novel model combining nonparametric stochastic volatility and deterministic shifts, with a local characteristic function expansion for efficient ultra-short-term option pricing.

Findings

Edgeworth++ accurately captures implied-volatility smiles across tenors.

The model provides fast, closed-form option pricing via Fourier inversion.

Compared to benchmarks, the approach offers improved flexibility and computational efficiency.

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. We derive a local (in tenor) expansion of the process characteristic function suited to value ultra-short-term options. The expansion leads to fast and accurate option pricing in closed form via standard Fourier inversion. We discuss the benefits of the proposed approach relative to benchmarks.