We calculate the leading term of asymptotics of the prices of barrier options and first touch digitals near the barrier for wide classes of Levy processes with exponential jump densities, including Variance Gamma model, KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes. In the case...

We analyze and compare the performance of the Fourier transform method in affine and quadratic term structure models. We explain why the method of the reduction to FFT in dimension 1 is efficient for ATSMs of type A0(n), but may lead to sizable errors for QTSMs unless computational errors are...

We show that three classes of multi-factor gaussian mean-reverting models: for the dynamics of the (log-)price of a stock, ATSM of the Ornstein-Uhlenbeck type, and QTSM are equivalent, when contingent claims with deterministic life-spans are considered. We provide the reduction of these models...

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...

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...

Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general, computationally simple approach to real options in discrete...