Search results for "difference"
showing 10 items of 1534 documents
An Iterative Method for Pricing American Options Under Jump-Diffusion Models
2011
We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou's and Merton's jump-diffusion models show that the resulting iteration converges rapidly.
An IMEX-Scheme for Pricing Options under Stochastic Volatility Models with Jumps
2014
Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps, especially for American-style option contracts. We consider the pricing of options under such models, namely the Bates model and the so-called stochastic volatility with contemporaneous jumps (SVCJ) model. The nonlocality of the jump terms in these models leads to matrices with full matrix blocks. Standard discretization methods are not viable directly since they would require the inversion of such a matrix. Instead, we adopt a two-step implicit-explicit (IMEX) time discretization scheme, the IMEX-CNAB scheme, where the jump term is treated ex…
Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
2004
A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.
Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation
2002
Abstract The detailed construction of a prefixed fundamental set of solutions of a linear homogeneous difference equation of any order with arbitrarily variable coefficients is reported. The usefulness of the resulting resolutive formula is illustrated by simple applications to the Hermite polynomials and to the Fibonacci sequence.
Improvement of matrix solutions of generalized nonlinear wave equation
2005
Four classes of nonlinear wave equations are joined in one generalized nonlinear wave equation. A theorem is proved that the whole series of matrix functions satisfy the generalized wave equation. A justification of rotational properties of matrix solutions is given and a mathematical model of the ring vortex around the acute edge is proposed using of matrix solutions.
Deep Learning Models Performance For NDVI Time Series Prediction: A Case Study On North West Tunisia
2020
The main goal of this paper is to analyze the performance of two deep learning models Long Short-Term Memory (LSTM) and bidirectional LSTM (BiLSTM) network for non-stationary Normalized Difference Vegetation Index (NDVI) time-series prediction. Both methods have provided good performances in the different time series. The BiLSTM has shown the best agreement with the lowest root mean square error (RMSE) and the highest Pearson correlation coefficient (R) of 0.034 and 0.93, respectively.
A Non-Local Two Dimensional Foundation Model
2012
Classical foundation models such as the Pasternak and the Reissner models have been recently reformulated within the framework of non-local mechanics, by using the gradient theory of elasticity. To contribute to the research effort in this field, this paper presents a two-dimensional foundation model built by using a mechanically based non-local elasticity theory, recently proposed by the authors. The foundation is thought of as an ensemble of soil column elements resting on an elastic base. It is assumed that each column element is acted upon by a local Winkler-like reaction force exerted by the elastic base, by contact shear forces and volume forces due, respectively, to adjacent and non-…
Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay
2010
Abstract An elastic continuum model with long-range forces is addressed in this study within the context of approximate analytical methods. Such a model stems from a mechanically-based approach to non-local theory where long-range central forces are introduced between non-adjacent volume elements. Specifically, long-range forces depend on the relative displacement, on the volume product between interacting elements and they are proportional to a proper, material-dependent, distance-decaying function. Smooth-decay functions lead to integro-differential governing equations whereas hypersingular, fractional-decay functions lead to a fractional differential governing equation of Marchaud type. …
Effects of Kinesiotape® taping on plantar pressure and impact acceleration during walking
2014
Summary Objectives The aim of this study was to analyse the plantar pressure pattern, contact time, stride rate and impact acceleration in the shank during walking with and without Kinesio Tape (KT®) placed on two muscle groups: peroneus and triceps surae. Methods Among the subjects, 29 (12 men, 17 women) participated in the study. KT® was placed on the triceps surae and peroneus and participants walked at two different speeds (V1: 0.73 m/s; V2: 1.30 m/s) with and without KT®. The pedobarographic system Biofoot IBV® 6.0 was used to analyse plantar pressure (mean peak pressure [kPa]) in 5 foot areas and the kinematic variables of the study (contact time [s]; stride rate [steps/second]). One …
Class-attendance and Online-tests Results: Reflections for Continuous Assessment
2020
Sometimes class-attendance is a component (or requirement) to benefit from the continuous assessment. The objective of this study is to evidence that some students seem to be getting unfairly penal...