We consider a fractional version of the Heston model where the two standard Brownian motions are replaced by two fractional Brownian motions with Hurst parameter H ∈ (1/2, 1). We show that the stochastic differential equation admits a unique positive solution by adapting and generalizing some...

A regime switching model in continuous time is introduced where a variety of jumps are allowed in addition to the diffusive component. The characteristic function of the process is derived in closed form, and is subsequently employed to create the likelihood function. In addition, standard...

This study investigates European option pricing under fractional Brownian motion (fBm) and applies it to realized volatility (RV). The RV measure is selected because it uniquely exhibits simultaneous stationarity and long-range dependency properties in financial time series, as shown in our...

We apply a new numerical method, the singular Fourier-Pade (SFP) method invented by Driscoll and Fornberg (2001, 2011), to price European-type options in Levy and affine processes. The motivation behind this application is to reduce the ineffciency of current Fourier techniques when they are...

Closed-form pricing formulae and option Greeks are obtained for European-type options using an orthogonal polynomial series -- complex Fourier series. We assume that risky assets are driven by exponential Lévy processes and stochastic volatility models. We provide a succinct error analysis to...

We show how spectral filtering techniques can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities,...

Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of European and path-dependent options in a fast mean-reverting stochastic volatility setting. Our method is shown to be equivalent to those developed...