Tempered Stable Distributions

The main topics covered in this chapter are:the history of the tempered stable distribution and why this distribution has been applied in finance;the main properties and formulas of tempered stable laws;the evaluation of the characteristic function in a non-trivial case (i.e., for the rapidly decreasing tempered stable law);probability density and cumulative distribution function evaluation when only the characteristic function is available in closed form while the density function is not;how to generate sample draws from a tempered stable distribution;how to estimate the parameters of a tempered stable distribution from a sample;how to evaluate well-known risk measures for a tempered stable stock market model.