We explicitly solve the pricing problem for perpetual American puts and calls, and provide an efficient semi-explicit pricing procedure for options with finite time horizon. Contrary to the standard approach, which uses the price process as a primitive, we model the price process as the expected...

Exponential growth of credit default swaps market and the resulting pile of CDS contracts of notional value of $62 trillion by the end of 2007 as well as the OTC nature of the contracts are widely believed to be one of the main causes of the current crisis and its depth, because large volumes of...

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...

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 review popular methods for pricing European options based on the Fourier expansion of the payoff function (iFT method) and the trapezoid rule, and suggest several new efficient variations. The first variation is a group of PMwFT methods (Payoff Modification with Fourier Transform), which...

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 derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical...

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...

Perturbation approach to pricing of contingent claims in affine and quadratic term structure models driven by processes Ornstein-Uhlenbeck type, with small jump components, is developed. For contingent claims of short maturity, the leading term and correction terms are calculated using the...