A Jump-Diffusion Model for Ultra-Short-Term Option Volatility

Summary

This document introduces Edgeworth++, a model for pricing options with maturities shorter than one week. The motivation is that at-the-money implied volatility can oscillate sharply across these short tenors, making joint pricing difficult for classical approaches. The model combines jump-diffusion dynamics with a nonparametric stochastic volatility component to capture volatility smiles within each tenor, then adds a deterministic shift to fit the term structure across tenors.

The authors derive a local expansion of the process characteristic function and use standard Fourier inversion to price options in closed form. They characterize the approach as fast and accurate and discuss it relative to benchmark models. The document gives no benchmark names, numerical results, data description, or implementation details, so the claimed performance cannot be independently assessed from this summary alone. Its stated scope is model-based valuation of ultra-short-term options, rather than a trading strategy.

Key ideas

• Ultra-short-term options exhibit pronounced oscillations in at-the-money implied volatility across tenors.
• Edgeworth++ combines jump-diffusion dynamics with nonparametric stochastic volatility.
• A deterministic shift extension allows the model to fit term-structure shapes across short tenors.
• A local characteristic-function expansion supports closed-form pricing through Fourier inversion.
• The document discusses benchmarks but supplies no quantitative comparison details.

Tags

# Ultra-short-term volatility surfaces


# Ultra-short-term volatility surfaces









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.