SIAM Journal on Scientific and Statistical Computing
Penalty methods for American options with stochastic volatility
Journal of Computational and Applied Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Computational Methods for Option Pricing (Frontiers in Applied Mathematics) (Frontiers in Applied Mathematics 30)
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
A Spectral Element Method to Price European Options. I. Single Asset with and without Jump Diffusion
Journal of Scientific Computing
Journal of Scientific Computing
High-order compact finite difference scheme for option pricing in stochastic volatility models
Journal of Computational and Applied Mathematics
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We develop a Legendre quadrilateral spectral element approximation for the Black-Scholes equation to price European options with one underlying asset and stochastic volatility. A weak formulation of the equations imposes the boundary conditions naturally along the boundaries where the equation becomes singular, and in particular, we use an energy method to derive boundary conditions at outer boundaries for which the problem is well-posed on a finite domain. Using Heston's analytical solution as a benchmark, we show that the spectral element approximation along with the proposed boundary conditions gives exponential convergence in the solution and the Greeks to the level of time and boundary errors in a domain of financial interest.