Pricing of geometric Asian options in the Volterra-Heston model
Florian Aichinger, Sascha Desmettre
TL;DR
The paper develops semi-analytic pricing formulas for geometric Asian options within the Volterra-Heston (including rough Heston) volatility framework. By representing the joint conditional Fourier transform of the log-price and the log-geometric mean as an exponential affine functional tied to forward variance and a Volterra Riccati equation, it extends classical Heston results to non-Markovian settings. The authors derive explicit pricing formulas for fixed- and floating-strike geometric Asian options and establish consistency with the classical Markovian case, supported by a thorough numerical study of the rough Heston model. The work leverages affine Volterra process theory to enable tractable computation and offers insight into how roughness impacts option values across maturities, with potential practical calibration benefits in markets exhibiting rough volatility.
Abstract
Geometric Asian options are a type of options where the payoff depends on the geometric mean of the underlying asset over a certain period of time. This paper is concerned with the pricing of such options for the class of Volterra-Heston models, covering the rough Heston model. We are able to derive semi-closed formulas for the prices of geometric Asian options with fixed and floating strikes for this class of stochastic volatility models. These formulas require the explicit calculation of the conditional joint Fourier transform of the logarithm of the stock price and the logarithm of the geometric mean of the stock price over time. Linking our problem to the theory of affine Volterra processes, we find a representation of this Fourier transform as a suitably constructed stochastic exponential, which depends on the solution of a Riccati-Volterra equation. Finally we provide a numerical study for our results in the rough Heston model.