Arbitrage-free prices $u$ of European contracts on risky assets whose log-returns are modelled by Lévy processes satisfy a parabolic partial integro-differential equation (PIDE) ${\partial }_{t}u+𝒜\left[u\right]=0$. This PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the $\theta$-scheme in time and a wavelet Galerkin method with $N$ degrees of freedom in log-price space. The dense matrix for $𝒜$ can be replaced by a sparse matrix in the wavelet basis, and the linear...

Arbitrage-free prices u of European contracts on risky assets whose log-returns are modelled by Lévy processes satisfy a parabolic partial integro-differential equation (PIDE) ${\partial }_{t}u+𝒜\left[u\right]=0$. This PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the θ-scheme in time and a wavelet Galerkin method with N degrees of freedom in log-price space. The dense matrix for $𝒜$ can be replaced by a sparse matrix in the wavelet basis, and the...

We study Fourier multipliers resulting from martingale transforms of general Lévy processes.