Quantitative Finance Lab

Hurst Exponent and Financial Market Predictability

QFinLab — Sat, 21 Jul 2012 08:45:15 +0000

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 for predictability.

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Authors
Bo Qian
Khaled Rasheed

A Fuzzy Approach to Real Option Valuation

QFinLab — Sat, 14 Jul 2012 08:52:54 +0000

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 (heuristic) real option rule in a fuzzy setting, where the present values of expected cash ﬂows and expected costs are estimated by trapezoidal fuzzy numbers. We shall determine the optimal exercise time by the help of possibilistic mean value and variance of fuzzy numbers.

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Authors
Christer Carlsson
Robert Fuller

Perspectives for Monte Carlo simulations on the CNN Universal Machine

QFinLab — Sat, 07 Jul 2012 04:55:28 +0000

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 the analog and parallel architecture of the CNN-UM is very appropriate for stochastic simulations on lattice models. The natural trend for increasing the number of cells and local memories on the CNN-UM chip will definitely favor in the near future the CNN-UM architecture for such problems.

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Authors:
M. Ercsey-Ravasz
T. Roska
Z. Neda

Forecasting Crude Oil Spot Price by WNN Using OECD Petroleum Inventory Levels

QFinLab — Sun, 01 Jul 2012 17:01:23 +0000

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, in-sample and out-of-sample prediction performance also demonstrates that the WNN-based forecasting model can produce more accurate prediction results than other nonlinear and linear models, even when the length of the forecast horizon is relatively short or long.

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Authors:
Ye Pang
Wei Xu
LeanYu
Jian Ma
Kin Keung Lai
Shouyang Wang
Shanying Xu

A Nonlinear PDE in Mathematical Finance

QFinLab — Sat, 23 Jun 2012 08:50:05 +0000

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 global solutions.

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Author
Sergio Polidoro

A Mixed PDE /Monte-Carlo Method for Stochastic Volatility Models

QFinLab — Sat, 12 May 2012 13:27:50 +0000

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 in the framework of the Heston stochastic volatility Model with and without barriers.

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Authors
Gregoire Loeper
Olivier Pironneau

Numerical Convergence Properties of Option Pricing PDEs with Uncertain Volatility

QFinLab — Sat, 21 Apr 2012 11:42:15 +0000

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 non-monotone discretization schemes (such as standard Crank-Nicolson timestepping) can converge to incorrect solutions, or lead to instability. Numerical examples are provided.

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Authors
D. M. Pooley
P. A. Forsyth
K. R. Vetzal

Forecasting Volatility Based on Wavelet Support Vector Machine

QFinLab — Sat, 14 Apr 2012 09:49:58 +0000

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 of wavelet support vector machine (WSVM) for volatility forecasting are conﬁrmed through computer simulations and experiments on realworld stock data.

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Authors
Ling-Bing Tang
Ling-Xiao Tang
Huan-Ye Sheng

A Dynamic Multivariate Heavy-tailed Model for Time-varying Volatilities and Correlations

QFinLab — Sat, 07 Apr 2012 19:24:23 +0000

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 estimates that are more robust to large innovations. The model also admits a representation as a time-varying heavy-tailed copula which is particularly useful if the interest focuses on dependence structures. We provide an empirical illustration for a panel of daily global equity returns.

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Authors
Drew Creal
Siem Jan Koopman
André Lucas

A Neural Economic Time Series Prediction with the Use of a Wavelet Analysis

QFinLab — Sat, 31 Mar 2012 21:29:58 +0000

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 USD/PLN average exchange rates. The achieved results are satisfactory.

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Author
Pawel Hajto