We derive a general formula for the time decay, theta, for out-of-the-money European options on stocks and bonds at expiry, in terms of the density of jumps and payoff. Explicit formulas are derived for the standard put and call options, exchange options in stochastic volatility and local...

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...

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...

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...

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...

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 derive a general formula for pricing options with barrier and/or lookback features, which covers several types of options studied in the literature and new types of options, and demonstrate that the pricing formula can be efficiently realized using the methodology developed in Kudryavtsev and...

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...