# The Heston stochastic volatility model has a boundary trace at zero volatility.

@article{Alziary2020TheHS, title={The Heston stochastic volatility model has a boundary trace at zero volatility.}, author={B'en'edicte Alziary and Peter Tak'avc}, journal={arXiv: Analysis of PDEs}, year={2020} }

We establish boundary regularity results in H\"older spaces for the degenerate parabolic problem obtained from the Heston stochastic volatility model in Mathematical Finance set up in the spatial domain (upper half-plane) $\mathbb{H} = \mathbb{R}\times (0,\infty)\subset \mathbb{R}^2$. Starting with nonsmooth initial data $u_0\in H$, we take advantage of smoothing properties of the parabolic semigroup $\mathrm{e}^{-t\mathcal{A}}\colon H\to H$, $t\in \mathbb{R}_+$, generated by the Heston model…

## One Citation

### Solution of option pricing equations using orthogonal polynomial expansion

- MathematicsApplications of Mathematics
- 2019

This paper uses a Galerkin-based method to solve the parabolic partial diferential equation for the Black-Scholes model using Hermite polynomials and for the Heston model usingHermite and Laguerre polynmials, and compares obtained solutions to existing semi-closed pricing formulas.

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