Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Journal of Computational Physics
Penalty methods for American options with stochastic volatility
Journal of Computational and Applied Mathematics
Quadratic Convergence for Valuing American Options Using a Penalty Method
SIAM Journal on Scientific Computing
A penalty method for American options with jump diffusion processes
Numerische Mathematik
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
SIAM Journal on Numerical Analysis
Anatomy of high-performance matrix multiplication
ACM Transactions on Mathematical Software (TOMS)
Numerical solution of two asset jump diffusion models for option valuation
Applied Numerical Mathematics
A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under Lévy Processes
SIAM Journal on Scientific Computing
A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pricing early-exercise and discrete barrier options by fourier-cosine series expansions
Numerische Mathematik
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We consider the problem of pricing American options in the framework of a well-known stochastic volatility model with jumps, the Bates model. According to this model the asset price is described by a jump-diffusion stochastic differential equation in which the jump term consists of a Levy process of compound Poisson type, while the volatility is modeled as a CIR-type process correlated with the asset price. Pricing American options under the Bates model requires us to solve a partial integro-differential equation with the final condition and boundary conditions prescribed on a free boundary. In this paper a numerical method for solving such a problem is proposed. In particular, first of all, using a Richardson extrapolation technique, the problem is reduced to a problem with fixed boundary. Then the problem obtained is solved using an ad hoc finite element method which efficiently combines an implicit/explicit time stepping, an operator splitting technique, and a non-uniform mesh of right-angled triangles. Numerical experiments are presented showing that the option pricing algorithm developed in this paper is extremely accurate and fast. In particular it is significantly more efficient than other numerical methods that have recently been proposed for pricing American options under the Bates model.