  We provide a bound for the error committed when using a Fourier method to
price European options when the underlying follows an exponential \levy
dynamic. The price of the option is described by a partial integro-differential
equation (PIDE). Applying a Fourier transformation to the PIDE yields an
ordinary differential equation that can be solved analytically in terms of the
characteristic exponent of the \levy process. Then, a numerical inverse Fourier
transform allows us to obtain the option price. We present a novel bound for
the error and use this bound to set the parameters for the numerical method. We
analyse the properties of the bound for a dissipative and pure-jump example.
The bound presented is independent of the asymptotic behaviour of option prices
at extreme asset prices. The error bound can be decomposed into a product of
terms resulting from the dynamics and the option payoff, respectively. The
analysis is supplemented by numerical examples that demonstrate results
comparable to and superior to the existing literature.
