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

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.