Work

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

Year: 2025

Type: article

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.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70075

Authors: José Da Fonseca, Wenjun Zhang

Institutions: Auckland University of Technology, PRISM Sorbonne, Université Paris 1 Panthéon-Sorbonne

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: $5,000

Funder: Auckland University of Technology, New Zealand