Tempered stable distributions and processes in finance: numerical analysis

Most of the important models in finance rest on the assumption that randomness is explained through a normal random variable. However there is ample empirical evidence against the normality assumption, since stock returns are heavy-tailed, leptokurtic and skewed. Partly in response to those empirical inconsistencies relative to the properties of the normal distribution, a suitable alternative distribution is the family of tempered stable distributions. In general, the use of infinitely divisible distributions is obstructed by the difficulty to calibrate and simulate them. In this paper, we address some numerical issues resulting from tempered stable modelling, with a view toward the density approximation and simulation. M.S.C. classification: 60E07.