A fast Monte Carlo scheme for additive processes and option pricing

In this paper, we present a very fast Monte Carlo scheme for additive processes: the computational time is of the same order of magnitude of standard algorithms for simulating Brownian motions. We analyze in detail numerical error sources and propose a technique that reduces the two major sources of error. We also compare our results with a benchmark method: the jump simulation with Gaussian approximation. We show an application to additive normal tempered stable processes, a class of additive processes that calibrates "exactly" the implied volatility surface. Numerical results are relevant. This fast algorithm is also an accurate tool for pricing path-dependent discretely-monitoring options with errors of one basis point or below.