Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models

We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have exponential utility functions and the individual endowments are spanned by the securities, an equilibrium exists and the agents' optimal trading strategies are constant. Affine processes, and the theory of information-based asset pricing are used to model the endogenous asset price dynamics and the terminal payoff. The derived semi-explicit pricing formulae are applied to numerically analyze the impact of the agents' risk aversion on the implied volatility of simultaneously-traded European-style options.Comment: 24 pages, 4 figure

Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.Comment: 9 pages, 2 figures, 1 tabl

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

A robust spectral method for solving Heston’s model

In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979)

A Subset of Replication Proteins Enhances Origin Recognition and Lytic Replication by the Epstein-Barr Virus ZEBRA Protein

ZEBRA is a site-specific DNA binding protein that functions as a transcriptional activator and as an origin binding protein. Both activities require that ZEBRA recognizes DNA motifs that are scattered along the viral genome. The mechanism by which ZEBRA discriminates between the origin of lytic replication and promoters of EBV early genes is not well understood. We explored the hypothesis that activation of replication requires stronger association between ZEBRA and DNA than does transcription. A ZEBRA mutant, Z(S173A), at a phosphorylation site and three point mutants in the DNA recognition domain of ZEBRA, namely Z(Y180E), Z(R187K) and Z(K188A), were similarly deficient at activating lytic DNA replication and expression of late gene expression but were competent to activate transcription of viral early lytic genes. These mutants all exhibited reduced capacity to interact with DNA as assessed by EMSA, ChIP and an in vivo biotinylated DNA pull-down assay. Over-expression of three virally encoded replication proteins, namely the primase (BSLF1), the single-stranded DNA-binding protein (BALF2) and the DNA polymerase processivity factor (BMRF1), partially rescued the replication defect in these mutants and enhanced ZEBRA's interaction with oriLyt. The findings demonstrate a functional role of replication proteins in stabilizing the association of ZEBRA with viral DNA. Enhanced binding of ZEBRA to oriLyt is crucial for lytic viral DNA replication