A Variational Formulation of European Option Prices in the 1‐Hypergeometric Stochastic Volatility Model
Date
Authors
Da Fonseca, Jose
Zhang, Wenjun
Supervisor
Item type
Journal Article
Degree name
Journal Title
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Volume Title
Publisher
Wiley
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.Description
Keywords
0102 Applied Mathematics, Applied Mathematics, 4901 Applied mathematics, European option, finite element method, stochastic volatility, variational method
Source
Mathematical Methods in the Applied Sciences, ISSN: 0170-4214 (Print); 1099-1476 (Online), Wiley. doi: 10.1002/mma.70075
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This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in anymedium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2025 The Author(s). Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd