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 prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Gaussian model with the same instantaneous variance. Numerical results are produced to show that for typical parameters values, the relative error of the Gaussian...

The non-gaussianity of processes observed in financial markets and relatively good performance of gaussian models can be reconciled by replacing the Brownian motion with Levy processes whose Levy densities exhibit exponential decay, and the rate of decay is large. This leads to asymptotic...

In this article we apply Carr's randomization approximation and the operator form of the Wiener-Hopf method to double barrier options in continuous time. Each step in the resulting backward induction algorithm is solved using a simple iterative procedure that reduces the problem of pricing...

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 $e^{i\Phi(-\sqrt{-1}\dd_x)}$...

Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around the line of integration in the complex plane.The Fourier transform techniques reduces calculation of probability distributions and option...

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 study sources of potentially serious errors of popular numerical realizations of the Fourier method in affine models, and explain that, in many cases, a calibration procedure based on such a realization will be able to find a "correct parameter set" only in a rather small region of the...

We present a fast and accurate FFT-based method of computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a Levy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the results...

The fast Fourier transform (FFT) technique is now a standard tool for the numerical calculation of prices of derivative securities. Unfortunately, in many important situations, such as the pricing of contingent claims of European type near expiry, and the pricing of barrier options close to the...