The Hurst exponent (H) is a statistical measure used to classify time series. H=0.5 indicates a random series while H>0.5 indicates a trend reinforcing series. The larger the H value is, the stronger trend. In this paper we investigate the use of the Hurst exponent to classify series of financial data representing different periods of time. Experiments with backpropagation Neural Networks show that series with large Hurst exponent can be predicted more accurately than those series with H value close to 0.50. Thus Hurst exponent provides a measure Read the rest of this entry »
To have a real option means to have the possibility for a certain period to either choose for or against making an invetsment decision, without binding oneself up front. The real option rule is that one should invest today only if the net present value is high enough to compensate for giving up the value of the option to wait. Because the option to invest loses its value when the investment is irreversibly made, this loss is an opportunity cost of investing. The main question that a management group must answer for a deferrable investment opportunity is: How long do we postpone the investment, if we can postpone it, up to T time periods? In this paper we shall introduce a Read the rest of this entry »
Possibilities for performing stochastic simulations on the analog and fully parallelized Cellular Neural Network Universal Machine (CNN-UM) are investigated. By using a chaotic cellular automaton perturbed with the natural noise of the CNN-UM chip, a realistic binary random number generator is built. As a specific example for Monte Carlo type simulations, we use this random number generator and a CNN template to study the classical site-percolation problem on the ACE16K chip. The study reveals that Read the rest of this entry »
In this study, a novel forecasting model based on Wavelet Neural Network (WNN) is proposed to predict monthly crude oil spot prices. In this new model, OECD industrial petroleum inventory levels are used as the independent variable, and Wavelet Neural Network (WNN) is used to model the nonlinear relationship between inventories and prices. For verification purpose, West Texas Intermediate (WTI) crude oil spot price is used. Experiment results reveal that WNN can model the nonlinear relationship between inventories and price very well. Furthermore, Read the rest of this entry »
We study a non linear degenerate Cauchy problem arising in mathematical finance. We prove the existence of a local strong solution and we study its regularity in the framework of subelliptic operators on nilpotent Lie groups. Moreover we give some conditions for the existence of Read the rest of this entry »
We propose a pricing method for derivatives modeled by a set of stochastic differential equations with the objective of reducing the computing time. The speed up observed in our numerical implementation can be as large as 50. The method is based on a joint use of Monte-Carlo simulations and PDE or analytical formulas. The method is tested Read the rest of this entry »
The pricing equations derived from uncertain volatility models in finance are often cast in the form of nonlinear partial differential equations. Implicit timestepping leads to a set of nonlinear algebraic equations which must be solved at each timestep. To solve these equations, an iterative approach is employed. In this paper, we prove the convergence of a particular iterative scheme for one factor uncertain volatility models. We also demonstrate how Read the rest of this entry »
One of the challenging problems in forecasting the conditional volatility of stock market returns is that general kernel functions in support vector machine (SVM) cannot capture the cluster feature of volatility accurately. While wavelet function yields features that describe of the volatility time series both at various locations and at varying time granularities, so this paper construct a multidimensional wavelet kernel function and prove it meeting the mercer condition to address this problem. The applicability and validity Read the rest of this entry »
We propose a new class of observation-driven time-varying parameter models for dynamic volatilities and correlations to handle time series from heavy-tailed distributions. The model adopts generalized autoregressive score dynamics to obtain a time-varying covariance matrix of the multivariate Student’s t distribution. The key novelty of our proposed model concerns the weighting of lagged squared innovations for the estimation of future correlations and volatilities. When we account for heavy tails of distributions, we obtain Read the rest of this entry »
The main theme of this article is the mathematical theory needed to develop a computer application that helps to predict economic data, which contain an element of time. This is the case of stock markets, currency exchange rates, inflation rates, etc. In the second part of this paper an example application and its forecasting results are described. The application was used to predict Read the rest of this entry »
