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September 5, 2025Open Access

A Variational Formulation of European Option Prices in the 1‐Hypergeometric Stochastic Volatility Model

JFJosé Da FonsecaAuckland University of Technology WZWenjun ZhangAuckland University of Technology

Key Points

The proposed method estimates the weak solution in a weighted Sobolev space.
Analysis using semigroup theory reveals constraints on model parameters.
Implementation includes a finite element method library to demonstrate the model's application.
The approach enhances understanding of pricing dynamics in stochastic volatility models.

Abstract

ABSTRACT The paper proposes a variational analysis of the 1‐hypergeometric stochastic volatility model for pricing European options. The methodology involves the derivation of estimates of the weak solution in a weighted Sobolev space. The weight is closely related to the stochastic volatility dynamic of the model. The solution is further analyzed using semigroup theory applied to the pricing operator and leads to certain constraints on the model parameters. An implementation of the model using a finite element method library is carried out and illustrates how the model works.

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