We develop a new method for pricing options on discretely sampled arithmetic average in exponential L'evy models. The main idea is the reduction to a backward induction procedure for the difference W_n between the Asian option with averaging over n sampling periods and the price of the European...

We consider discretely monitored barrier options under Levy models, including single and double barrier options and first touch digitals, as well as CDS and defaultable bonds. At each step of backward induction, we use piece-wise polynomial interpolation and an efficient version of the Fourier...

For prices of options with barrier and lookback features, defaultable bonds and CDS, and probability distribution functions in Levy models, joint probability distributions of the process and its supremum or/and infimum, one can derive explicit analytical formulas in terms of the Laplace...

Recently, the advantages of conformal deformations of the contours of integration in pricing formulas were demonstrated in the context of wide classes of Levy models and the Heston model. In the present paper we construct efficient conformal deformations of the contours of integration in the...

We suggest a general scheme for improvement of FT-pricing formulas for European option and give efficient recommendations for the choice of the parameters of the numerical scheme, which allow for very accurate and fast calculations. The efficiency of the method stems from the properties of...

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 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...

The standard operator approach to the identification problem of diffusions and more general Markov processes relies on the variational principles for self-adjoint operators. If the process is not time reversible, equivalently, the infinitesimal operator of the process is not self-adjoint, these...