We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable (Y/2) subordinator while the Meixner time change is absolutely continuous with respect to the one sided stable (1/2) subordinator. The required time changes may be generated by simulating the requisite one-sided stable subordinator a...

The goal of the paper is to show that some types of Lévy processes such as the hyperbolic motion and the CGMY are particularly suitable for asset price modelling and option pricing. We wish to review some fundamental mathematic properties of Lévy distributions, such as the one of infinite divisibility, and how they translate observed features of asset price returns. We explain how these process...

The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY Lévy process. This allows, for the approximation , exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral process for which we infer the first passage times of stock prices to 30% o...

This paper proposes the sample path generation method for stochastic volatility version of CGMY process. We present Monte-Carlo European and American option pricing with calibrate model parameters to style S&P 100 index options market, using least square regression method. Moreover, we discuss path-dependent options, such as Asian Barrier options.