Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized superdiffusive regime is established. This is verified by showing that the square width of the probability distribution (appropriately defined)grows as t 2/γ with 0 < γ ≤...

Abstract. We present a method to apply the Malliavin calculus to calculate sensitivities for exponential Levy models built from the Variance Gamma and Normal Inverse Gaussian processes. We also present new sensitivities for these processes. The calculation of the sensitivities is based on a finite dimensional Malliavin calculus and we compare the results with finite difference calculations. Thi...

The Lévy walk hypothesis asserts that the optimal search strategy for a forager under specific conditions is to make successive movement steps that have uniformly random directions and lengths drawn from a probability distribution that is heavy-tailed. This idea has generated a huge amount of interest, with numerous studies providing empirical evidence in support of the hypothesis and others cr...

The availability of intraday stock/index return in the web facilitates the improvement of return volatility estimation over the traditional method that is based on inter-day return data. Truncated Levy process distribution is used to extract the intraday return distribution parameters. The calibration to the volatility for Black-Scholes option pricing is studied using the data from Levy-Gaussia...

We review the commonly used numerical algorithms for option pricing under Levy process via Fast Fourier transform (FFT) calculations. By treating option price analogous to a probability density function, option prices across the whole spectrum of strikes can be obtained via FFT calculations. We also show how the property of the Fourier transform of a convolution product can be used to value var...