Work

Pricing of geometric Asian options in the Volterra-Heston model

Year: 2025

Type: article

Abstract: Geometric Asian options are a type of option 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.

Source: Review of Derivatives Research

DOI: 10.1007/s11147-025-09211-w

Authors: Florian Aichinger, Sascha Desmettre

Institutions: Johannes Kepler University of Linz, Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Johannes Kepler Universität Linz, Austrian Science Fund