1. Let W denote the standard Brownian motion; we can construct a L�vyprocess by 'replacing' the (calendar) time t by an independent increasing L�vyprocess ?, therefore L t := W ?(t) , 0 ? t ? T . The process ? has the useful -in Finance -interpretation as 'business time'. Models constructed this way include the normal inverse Gaussian process, where Brownian motion is time-changed with the inverse Gaussian process and the variance gamma process;Time-changing Brownian motion with an independent increasing L�vyprocess
2. L�vyjump-di?usions) and some special cases of infinite activity L�vyprocesses, namely the normal inverse Gaussian and the variance gamma processes. Several speed-up methods for the Monte Carlo simulation of L�vyprocesses are presented in Webber05. Here, we do not discuss simulation methods for random variables with known density; various algorithms can be found in Devroye86;We shall briefly describe simulation methods for L�vyprocesses. Our attention is focused on finite activity L�vyprocesses (i.e