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 Lévy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the...

We study in this paper the extremal behavior of stochastic integrals of Legendre polynomial transforms with respect to Brownian motion. As the main results, we obtain the exact tail behavior of the supremum of these integrals taken over intervals [0,h] with h0 fixed, and the limiting...

Let G={G(x),x[set membership, variant]R1} be a mean zero Gaussian process with stationary increments and set [sigma]2(x-y)=E(G(x)-G(y))2. Let f be a symmetric function with Ef2([eta])[infinity], where [eta]=N(0,1). When [sigma]2(s) is concave or when [sigma]2(s)=sr, 1r=3/2, where...

We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian...

An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state x as x and |x|α. An exactly soluble model of a system is constructed due to consideration of a specific relation between noises. Exact expressions...

We have analyzed diffusion in a double well potential driven by a colored non-Gaussian noise. Using a path-integral approach we have obtained a consistent Markovian approximation to the initially non-Markovian problem. Such an approximation allows us to get analytical expressions for the...

Stochastic volatility and jumps are viewed as arising from Brownian subordination given here by an independent purely discontinuous process and we inquire into the relation between the realized variance or quadratic variation of the process and the time change. The class of models considered...