Numerical Simulations of Fractionated Electrograms and Pathological Cardiac Action Potential

The aim of this work is twofold. First we focus on the complex phenomenon of electrogram fractionation, due to the presence of discontinuities in the conduction properties of the cardiac tissue in a bidomain model. Numerical simulations of paced activation may help to understand the role of the membrane ionic currents and of the changes in cellular coupling in the formation of conduction blocks and fractionation of the electrogram waveform. In particular, we show that fractionation is independent ofINAalterations and that it can be described by the bidomain model of cardiac tissue. Moreover, some deflections in fractionated electrograms may give nonlocal information about the shape of damaged areas, also revealing the presence of inhomogeneities in the intracellular conductivity of the medium at a distance.The second point of interest is the analysis of the effects of space–time discretization on numerical results, especially during slow conduction in damaged cardiac tissue. Indeed, large discretization steps can induce numerical artifacts such as slowing down of conduction velocity, alteration in extracellular and transmembrane potential waveforms or conduction blocks, which are not predicted by the continuous bidomain model. Several possible numerical and physiological explanations of these effects are given. Essentially, the discrete system obtained at the end of the approximation process may be interpreted as a discrete model of the cardiac tissue made up of isopotential cells where the effective intracellular conductivity tensor depends on the space discretization steps; the increase of these steps results in an increase of the effective intracellular resistance and can induce conduction blocks if a certain critical value is exceeded

An Early Warning System for identifying financial instability

Financial crises prediction is an essential topic in finance. Designing an efficient Early Warning System (EWS) can help prevent catastrophic losses resulting from financial crises. We propose different EWSs for predicting potential market instability conditions, where market instability refers to large asset price declines. A logit regression EWS is employed to predict future large price losses and Early Warning Indicators (EWIs) based on the realized variance (RV) and price-volatility feedback rate are considered. The latter EWI is supposed to describe the ease of the market in absorbing small price perturbations. Our study reveals that, while RV is important in predicting future price losses in a given time series, the EWI employing the price-volatility feedback rate can improve prediction further

Stochastic leverage effect in high-frequency data: a Fourier based analysis

The stochastic leverage effect, defined as the standardized covariation between the returns and their related volatility, is analyzed in a stochastic volatility model set-up. A novel estimator of the effect is defined using a pre-estimation of the Fourier coefficients of the return and the volatility processes. The consistency of the estimator is proven. Moreover, its finite sample properties are studied in the presence of microstructure noise effects. The Fourier methodology is applied to S\&P500 futures prices to investigate the magnitude of the stochastic leverage effect detectable at high-frequency.Comment: Accepted for publication in Econometrics and Statistic

A fractional model for the COVID-19 pandemic: Application to Italian data

We provide a probabilistic SIRD model for the COVID-19 pandemic in Italy, where we allow the infection, recovery and death rates to be random. In particular, the underlying random factor is driven by a fractional Brownian motion. Our model is simple and needs only some few parameters to be calibrated.Comment: 20 pages, 26 figure

Calibration of a nonlinear feedback option pricing model

We consider the option pricing model proposed by Mancino and Ogawa, where the implementation of dynamic hedging strategies has a feedback impact on the price process of the underlying asset. We present numerical results showing that the smile and skewness patterns of implied volatility can actually be reproduced as a consequence of dynamical hedging. The simulations are performed using a suitable semi-implicit finite difference method. Moreover, we perform a calibration of the nonlinear model to market data and we compare it with more popular models, such as the Black-Scholes formula, the Jump-Diffusion model and Heston's model. In judging the alternative models, we consider the following issues: (i) the consistency of the implied structural parameters with the times-series data; (ii) out-of-sample pricing; and (iii) parameter uniformity across different moneyness and maturity classes. Overall, nonlinear feedback due to hedging strategies can, at least in part, contribute to the explanation from a theoretical and quantitative point of view of the strong pricing biases of the Black-Scholes formula, although stochastic volatility effects are more important in this regard.Option pricing, Numerical methods for option pricing, Partial differential equations, Implied volatilities, Option pricing via simulation, Parameter estimation techniques, Quantitative finance,

Optimal impulse control on an unbounded domain with nonlinear cost functions

In this paper we consider the optimal impulse control of a system which evolves randomly in accordance with a homogeneous diffusion process in ℜ 1. Whenever the system is controlled a cost is incurred which has a fixed component and a component which increases with the magnitude of the control applied. In addition to these controlling costs there are holding or carrying costs which are a positive function of the state of the system. Our objective is to minimize the expected discounted value of all costs over an infinite planning horizon. Under general assumptions on the cost functions we show that the value function is a weak solution of a quasi-variational inequality and we deduce from this solution the existence of an optimal impulse policy. The computation of the value function is performed by means of the Finite Element Method on suitable truncated domains, whose convergence is discussed. Copyright Springer-Verlag Berlin/Heidelberg 2006Impulse control, stochastic cash management, quasi-variational inequalities, finite element approximation,

FAST NUMERICAL PRICING OF BARRIER OPTIONS UNDER STOCHASTIC VOLATILITY AND JUMPS

In this paper, we prove the existence of an integral closed-form solution for pricing barrier options in both Heston and Bates frameworks. The option value depends on time, on the price and on the volatility of the underlying asset and it can be computed as the solution of a two dimensional pricing partial integro-differential equation. The integral representation formula of the solution is derived by projection of the differential equation and exploiting the properties of the adjoint operator. We derive the expression of the fundamental solution (Green's function) necessary for the integral representation formula. The computation is based on the interpretation of the fundamental solution as the joint transition probability density function of the underlying asset price and variance and is obtained through Fourier inverse transform of a suitable conditional characteristic function. We propose a numerical scheme to approximate the option price based on the classical Boundary Element Method and we provide two numerical examples showing the computational efficiency and accuracy of the proposed new method. The algorithm can be modified to compute greeks as well