We develop a general simple methodology for very fast and accurate evaluation of integrals of functions that admit analytic continuation into wide regions of the complex plane or into appropriate Riemann surfaces. We use a family of fractional-parabolic deformations of the contours of...

We suggest new efficient integral representations and methods for evaluation of pdfs, cpds and quantiles of stable distributions. For wide regions in the parameter space, absolute errors of order 10 can be achieved in 0.005-0.1 msec (Matlab implementation), even when the index of the...

We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model with an operator of the form $e^{i\Phi(-\sqrt{-1}\dd_x)}$...

Fast Fourier transform (FFT) method is now a standard calibration engine. However, in many situations, such as pricing of deep out-of-the-money European options, FFT produces large errors. We propose fast and accurate realizations of Integration-Along-Cut method (IAC method), which explicitly...

Barrier options under wide classes of L\'evy processes with exponential jump densities, including Variance Gamma model, KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes, are studied. The leading term of asymptotics of the option price and the leading term of asymptotics in Carr's...

We calculate the leading term of asymptotics of the prices of barrier options and first touch digitals near the barrier for wide classes of Levy processes with exponential jump densities, including Variance Gamma model, KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes. In the case...

The pricing problem for American options in Markov-modulated Lévy models is solved. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization procedure for regime-switching models. The pricing procedure is efficient even if the number of states is...