High-frequency dynamics of the implied volatility surface

TL;DR

This paper models the high-frequency dynamics of the implied volatility surface using Hawkes processes, revealing how kernel coefficients influence surface shape and ensuring no-arbitrage conditions, with implications for risk factor analysis.

Contribution

It introduces a Hawkes process framework for modeling the volatility surface's high-frequency behavior, linking kernel parameters to surface shape and arbitrage constraints.

Findings

Hawkes kernel coefficients govern skew and convexity.

Sufficient conditions for no-arbitrage are provided.

Surface driven by rough volatility risk factors.

Abstract

We present a Hawkes modeling of the volatility surface's high-frequency dynamics and show how the Hawkes kernel coefficients govern the surface's skew and convexity. We provide simple sufficient conditions on the coefficients to ensure no-arbitrage opportunities of the surface. Moreover, these conditions reduce the number of the kernel's parameters to estimate. Finally, we show that at the macroscopic level, the surface is driven by a sum of risk factors whose volatility processes are rough.