A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest...

We construct a new approximate method for pricing barrier options and CDSs. In many cases, prices of barrier options and CDSs of maturities one year and more, at the log-distance 0.1 from the barrier and farther, for 8 spots, can be calculated adding up 4-16 fairly simple terms, with relative...

We develop a general simple methodology for very fast and accurate evaluation of special functions of several classes. We use a family of fractional-parabolic deformations of the contours of integration to appropriate Riemann surfaces, make the corresponding conformal changes of variables and...

We generalize the Piterbarg (2010) model to include 1) bilateral default risk as in Burgard and Kjaer (2012), and 2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options...

Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of L'evy models, the Heston model and other affine models. Similar deformations were used in one-factor L'evy models to...

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...

A backward induction procedure for pricing arithmetic Asian options in Levy models is realized in the dual space. Each step of the procedure is the composition of a multiplication operators by an explicitly given function, and the convolution operator ${\cal H}_\Ga$, which belongs to a class 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 new families of integral representations of pdfs and cpds of stable distributions, which lead to efficient numerical methods. The first method is based on the approximation of the characteristic exponent by functions analytic in the complex plane with two cuts i(-∞,-λ] and i[λ,...