Search results for: Relative volatility
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 781

Search results for: Relative volatility

781 Forecasting the Volatility of Geophysical Time Series with Stochastic Volatility Models

Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

Abstract:

This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model.

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780 Volatility Model with Markov Regime Switching to Forecast Baht/USD

Authors: N. Sopipan, A. Intarasit, K. Chuarkham

Abstract:

 In this paper, we forecast the volatility of Baht/USDs using Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecasting Baht/USD volatility. The MRS-GARCH is the best performance model for Baht/USD volatility in short term but the GARCH model is best perform for long term.

Keywords: Volatility, Markov Regime Switching, Forecasting.

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779 Volatility of Cu, Ni, Cr, Co, Pb, and As in Fluidised-Bed Combustion Chamber in Relation to Their Modes of Occurrence in Coal

Authors: L. Bartoňová, Z. Klika

Abstract:

Modes of occurrence of Pb, As, Cr, Co, Cu, and Ni in bituminous coal and lignite were determined by means of sequential extraction using NH4OAc, HCl, HF and HNO3 extraction solutions. Elemental affinities obtained were then evaluated in relation to volatility of these elements during the combustion of these coals in two circulating fluidised-bed power stations. It was found out that higher percentage of the elements bound in silicates brought about lower volatility, while higher elemental proportion with monosulphides association (or bound as exchangeable ion) resulted in higher volatility. The only exception was the behavior of arsenic, whose volatility depended on amount of limestone added during the combustion process (as desulphurisation additive) rather than to its association in coal.

Keywords: Coal combustion, sequential extraction, trace elements, volatility.

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778 Implied Adjusted Volatility by Leland Option Pricing Models: Evidence from Australian Index Options

Authors: Mimi Hafizah Abdullah, Hanani Farhah Harun, Nik Ruzni Nik Idris

Abstract:

With the implied volatility as an important factor in financial decision-making, in particular in option pricing valuation, and also the given fact that the pricing biases of Leland option pricing models and the implied volatility structure for the options are related, this study considers examining the implied adjusted volatility smile patterns and term structures in the S&P/ASX 200 index options using the different Leland option pricing models. The examination of the implied adjusted volatility smiles and term structures in the Australian index options market covers the global financial crisis in the mid-2007. The implied adjusted volatility was found to escalate approximately triple the rate prior the crisis.

Keywords: Implied adjusted volatility, Financial crisis, Leland option pricing models.

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777 Using Exponential Lévy Models to Study Implied Volatility patterns for Electricity Options

Authors: Pinho C., Madaleno M.

Abstract:

German electricity European options on futures using Lévy processes for the underlying asset are examined. Implied volatility evolution, under each of the considered models, is discussed after calibrating for the Merton jump diffusion (MJD), variance gamma (VG), normal inverse Gaussian (NIG), Carr, Geman, Madan and Yor (CGMY) and the Black and Scholes (B&S) model. Implied volatility is examined for the entire sample period, revealing some curious features about market evolution, where data fitting performances of the five models are compared. It is shown that variance gamma processes provide relatively better results and that implied volatility shows significant differences through time, having increasingly evolved. Volatility changes for changed uncertainty, or else, increasing futures prices and there is evidence for the need to account for seasonality when modelling both electricity spot/futures prices and volatility.

Keywords: Calibration, Electricity Markets, Implied Volatility, Lévy Models, Options on Futures, Pricing

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776 The Impact of Exchange Rate Volatility on Real Total Export and Sub-Categories of Real Total Export of Malaysia

Authors: Wong Hock Tsen

Abstract:

This study aims to investigate the impact of exchange rate volatility on real export in Malaysia. The moving standard deviation with order three (MSD(3)) is used for the measurement of exchange rate volatility. The conventional and partially asymmetric autoregressive distributed lag (ARDL) models are used in the estimations. This study finds exchange rate volatility to have significant impact on real total export and some sub-categories of real total export. Moreover, this study finds that the positive or negative exchange rate volatility tends to have positive or negative impact on real export. Exchange rate volatility can be harmful to export of Malaysia.

Keywords: Exchange rate volatility, autoregressive distributed lag, export, Malaysia.

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775 The Applications of Quantum Mechanics Simulation for Solvent Selection in Chemicals Separation

Authors: Attapong T., Hong-Ming Ku, Nakarin M., Narin L., Alisa L, Jirut W.

Abstract:

The quantum mechanics simulation was applied for calculating the interaction force between 2 molecules based on atomic level. For the simple extractive distillation system, it is ternary components consisting of 2 closed boiling point components (A,lower boiling point and B, higher boiling point) and solvent (S). The quantum mechanics simulation was used to calculate the intermolecular force (interaction force) between the closed boiling point components and solvents consisting of intermolecular between A-S and B-S. The requirement of the promising solvent for extractive distillation is that solvent (S) has to form stronger intermolecular force with only one component than the other component (A or B). In this study, the systems of aromatic-aromatic, aromatic-cycloparaffin, and paraffindiolefin systems were selected as the demonstration for solvent selection. This study defined new term using for screening the solvents called relative interaction force which is calculated from the quantum mechanics simulation. The results showed that relative interaction force gave the good agreement with the literature data (relative volatilities from the experiment). The reasons are discussed. Finally, this study suggests that quantum mechanics results can improve the relative volatility estimation for screening the solvents leading to reduce time and money consuming

Keywords: Extractive distillation, Interaction force, Quamtum mechanic, Relative volatility, Solvent extraction.

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774 Statistical Computational of Volatility in Financial Time Series Data

Authors: S. Al Wadi, Mohd Tahir Ismail, Samsul Ariffin Abdul Karim

Abstract:

It is well known that during the developments in the economic sector and through the financial crises occur everywhere in the whole world, volatility measurement is the most important concept in financial time series. Therefore in this paper we discuss the volatility for Amman stocks market (Jordan) for certain period of time. Since wavelet transform is one of the most famous filtering methods and grows up very quickly in the last decade, we compare this method with the traditional technique, Fast Fourier transform to decide the best method for analyzing the volatility. The comparison will be done on some of the statistical properties by using Matlab program.

Keywords: Fast Fourier transforms, Haar wavelet transform, Matlab (Wavelet tools), stocks market, Volatility.

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773 Credit Spread Changes and Volatility Spillover Effects

Authors: Thomas I. Kounitis

Abstract:

The purpose of this paper is to investigate the influence of a number of variables on the conditional mean and conditional variance of credit spread changes. The empirical analysis in this paper is conducted within the context of bivariate GARCH-in- Mean models, using the so-called BEKK parameterization. We show that credit spread changes are determined by interest-rate and equityreturn variables, which is in line with theory as provided by the structural models of default. We also identify the credit spread change volatility as an important determinant of credit spread changes, and provide evidence on the transmission of volatility between the variables under study.

Keywords: Credit spread changes, GARCH-in-Mean models, structural framework, volatility transmission.

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772 Normalizing Logarithms of Realized Volatility in an ARFIMA Model

Authors: G. L. C. Yap

Abstract:

Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.

Keywords: Long-memory, Gaussian process, Whittle estimator, normalization, volatility, value-at-risk.

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771 Efficient Frontier - Comparing Different Volatility Estimators

Authors: Tea Poklepović, Zdravka Aljinović, Mario Matković

Abstract:

Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and compares three efficient frontiers on the Croatian Stock Market. The results show that range-based volatility estimator outperforms both mean-variance and lower semi-variance model.

Keywords: Variance, lower semi-variance, range-based volatility.

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770 The Influence of EU Regulation of Margin Requirements on Market Stock Volatility

Authors: Nadira Kaimova

Abstract:

In this paper it was examined the influence of margin regulation on stock market volatility in EU 1993 – 2014. Regulating margin requirements or haircuts for securities financing transactions has for a long time been considered as a potential tool to limit the build-up of leverage and dampen volatility in financial markets. The margin requirement dictates how much investors can borrow against these securities. Margin can be an important part of investment. Using daily and monthly stock returns and there is no convincing evidence that EU Regulation margin requirements have served to dampen stock market volatility. In this paper was detected the expected negative relation between margin requirements and the amount of margin credit outstanding. Also, it confirmed that changes in margin requirements by the EU regulation have tended to follow than lead changes in market volatility. For the analysis have been used the modified Levene statistics to test whether the standard deviation of stock returns in the 25, 50 and 100 days preceding margin changes is the same as that in the succeeding 25, 50 and 100 days. The analysis started in May 1993 when it was first empowered to set the initial margin requirement and the last sample was in May 2014. To test whether margin requirements influence stock market volatility over the long term, the sample of stock returns was divided into 14 periods, according to the 14 changes in margin requirements.

Keywords: Levene statistic, Margin Regulation, Stock Market, Volatility.

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769 Volatility Switching between Two Regimes

Authors: Josip Visković, Josip Arnerić, Ante Rozga

Abstract:

Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models. When financial returns exhibit sudden jumps that are due to structural breaks, standard GARCH models show high volatility persistence, i.e. integrated behavior of the conditional variance. In such situations models in which the parameters are allowed to change over time are more appropriate. This paper compares different GARCH models in terms of their ability to describe structural changes in returns caused by financial crisis at stock markets of six selected central and east European countries. The empirical analysis demonstrates that Markov regime switching GARCH model resolves the problem of excessive persistence and outperforms uni-regime GARCH models in forecasting volatility when sudden switching occurs in response to financial crisis.

Keywords: Central and east European countries, financial crisis, Markov switching GARCH model, transition probabilities.

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768 VaR Forecasting in Times of Increased Volatility

Authors: Ivo Jánský, Milan Rippel

Abstract:

The paper evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the ARMA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting accuracy is evaluated on the out-of-sample data, which are more volatile. The main aim of the paper is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index separately. The primary result of the paper is that the volatility is best modelled using a GARCH process and that an ARMA process pattern cannot be found in analyzed time series.

Keywords: VaR, risk analysis, conditional volatility, garch, egarch, tarch, moving average process, autoregressive process

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767 Performance of Heterogeneous Autoregressive Models of Realized Volatility: Evidence from U.S. Stock Market

Authors: Petr Seďa

Abstract:

This paper deals with heterogeneous autoregressive models of realized volatility (HAR-RV models) on high-frequency data of stock indices in the USA. Its aim is to capture the behavior of three groups of market participants trading on a daily, weekly and monthly basis and assess their role in predicting the daily realized volatility. The benefits of this work lies mainly in the application of heterogeneous autoregressive models of realized volatility on stock indices in the USA with a special aim to analyze an impact of the global financial crisis on applied models forecasting performance. We use three data sets, the first one from the period before the global financial crisis occurred in the years 2006-2007, the second one from the period when the global financial crisis fully hit the U.S. financial market in 2008-2009 years, and the last period was defined over 2010-2011 years. The model output indicates that estimated realized volatility in the market is very much determined by daily traders and in some cases excludes the impact of those market participants who trade on monthly basis.

Keywords: Global financial crisis, heterogeneous autoregressive model, in-sample forecast, realized volatility, U.S. stock market.

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766 Information Transmission between Large and Small Stocks in the Korean Stock Market

Authors: Sang Hoon Kang, Seong-Min Yoon

Abstract:

Little attention has been paid to information transmission between the portfolios of large stocks and small stocks in the Korean stock market. This study investigates the return and volatility transmission mechanisms between large and small stocks in the Korea Exchange (KRX). This study also explores whether bad news in the large stock market leads to a volatility of the small stock market that is larger than the good news volatility of the large stock market. By employing the Granger causality test, we found unidirectional return transmissions from the large stocks to medium and small stocks. This evidence indicates that pat information about the large stocks has a better ability to predict the returns of the medium and small stocks in the Korean stock market. Moreover, by using the asymmetric GARCH-BEKK model, we observed the unidirectional relationship of asymmetric volatility transmission from large stocks to the medium and small stocks. This finding suggests that volatility in the medium and small stocks following a negative shock in the large stocks is larger than that following a positive shock in the large stocks.

Keywords: Asymmetric GARCH-BEKK model, Asymmetric volatility transmission, Causality, Korean stock market, Spillover effect

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765 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

Authors: Chao Yuan, Bao Guang Tian

Abstract:

A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.

Keywords: Generalized linear model, generalized relative coefficient, least eigenvalue, relative efficiency.

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764 An Engineering Approach to Forecast Volatility of Financial Indices

Authors: Irwin Ma, Tony Wong, Thiagas Sankar

Abstract:

By systematically applying different engineering methods, difficult financial problems become approachable. Using a combination of theory and techniques such as wavelet transform, time series data mining, Markov chain based discrete stochastic optimization, and evolutionary algorithms, this work formulated a strategy to characterize and forecast non-linear time series. It attempted to extract typical features from the volatility data sets of S&P100 and S&P500 indices that include abrupt drops, jumps and other non-linearity. As a result, accuracy of forecasting has reached an average of over 75% surpassing any other publicly available results on the forecast of any financial index.

Keywords: Discrete stochastic optimization, genetic algorithms, genetic programming, volatility forecast

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763 The Effect of Oil Price Uncertainty on Food Price in South Africa

Authors: Goodness C. Aye

Abstract:

This paper examines the effect of the volatility of oil prices on food price in South Africa using monthly data covering the period 2002:01 to 2014:09. Food price is measured by the South African consumer price index for food while oil price is proxied by the Brent crude oil. The study employs the GARCH-in-mean VAR model, which allows the investigation of the effect of a negative and positive shock in oil price volatility on food price. The model also allows the oil price uncertainty to be measured as the conditional standard deviation of a one-step-ahead forecast error of the change in oil price. The results show that oil price uncertainty has a positive and significant effect on food price in South Africa. The responses of food price to a positive and negative oil price shocks is asymmetric.

Keywords: Oil price volatility, Food price, Bivariate GARCH-in- mean VAR, Asymmetric.

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762 Risk Management Analysis: An Empirical Study Using Bivariate GARCH

Authors: Chin Wen Cheong

Abstract:

This study employs a bivariate asymmetric GARCH model to reveal the hidden dynamics price changes and volatility among the emerging markets of Thailand and Malaysian after the Asian financial crisis from January 2001 to December 2008. Our results indicated that the equity markets are sharing the common information (shock) that transmitted among each others. These empirical findings are used to demonstrate the importance of shock and volatility dynamic transmissions in the cross-market hedging and market risk.

Keywords: multivariate ARCH, structural change, value at risk.

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761 A Study of Relationship between WBGT and Relative Humidity to Worker Performance

Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman

Abstract:

The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.

Keywords: WBGT, Relative Humidity, Comfort, Productivity.

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760 The Relative Efficiency Based on the MSE in Generalized Ridge Estimate

Authors: Chao Yuan, Bao Guang Tian

Abstract:

A relative efficiency is defined as Ridge Estimate in the general linear model. The relative efficiency is based on the Mean square error. In this paper, we put forward a parameter of Ridge Estimate and discussions are made on the relative efficiency between the ridge estimation and the General Ridge Estimate. Eventually, this paper proves that the estimation is better than the general ridge estimate, which is based on the MSE.

Keywords: Ridge estimate, generalized ridge estimate, MSE, relative efficiency.

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759 The Study of Relative Efficiency in Growth Curve Model

Authors: Nan Chen, Baoguang Tian

Abstract:

In this paper, some relative efficiency have been discussed, including the LSE estimate with respect to BLUE in curve model. Four new kinds of relative efficiency have defined, and their upper bounds have been discussed.

Keywords: Relative efficiency, LSE estimate, BLUE estimate, Upper bound, Curve model.

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758 Relative Navigation with Laser-Based Intermittent Measurement for Formation Flying Satellites

Authors: Jongwoo Lee, Dae-Eun Kang, Sang-Young Park

Abstract:

This study presents a precise relative navigational method for satellites flying in formation using laser-based intermittent measurement data. The measurement data for the relative navigation between two satellites consist of a relative distance measured by a laser instrument and relative attitude angles measured by attitude determination. The relative navigation solutions are estimated by both the Extended Kalman filter (EKF) and unscented Kalman filter (UKF). The solutions estimated by the EKF may become inaccurate or even diverge as measurement outage time gets longer because the EKF utilizes a linearization approach. However, this study shows that the UKF with the appropriate scaling parameters provides a stable and accurate relative navigation solutions despite the long measurement outage time and large initial error as compared to the relative navigation solutions of the EKF. Various navigation results have been analyzed by adjusting the scaling parameters of the UKF.

Keywords: Satellite relative navigation, laser-based measurement, intermittent measurement, unscented kalman filter.

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757 Investigating the UAE Residential Valuation System: A Framework for Analysis

Authors: Simon Huston, Ebraheim Lahbash, Ali Parsa

Abstract:

The development of the United Arab Emirates (UAE) into a regional trade, tourism, finance and logistics hub has transformed its real estate markets. However, speculative activity and price volatility remain concerns. UAE residential market values (MV) are exposed to fluctuations in capital flows and migration which, in turn, are affected by geopolitical uncertainty, oil price volatility and global investment market sentiment. Internally, a complex interplay between administrative boundaries, land tenure, building quality and evolving location characteristics fragments UAE residential property markets. In short, the UAE Residential Valuation System (UAE-RVS) confronts multiple challenges to collect, filter and analyze relevant information in complex and dynamic spatial and capital markets. A robust (RVS) can mitigate the risk of unhelpful volatility, speculative excess or investment mistakes. The research outlines the institutional, ontological, dynamic and epistemological issues at play. We highlight the importance of system capabilities, valuation standard salience and stakeholders trust.

Keywords: Valuation, property rights, information, institutions, trust, salience.

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756 Estimation of Relative Self-Localization Based On Natural Landmark and an Improved SURF

Authors: Xing Xiong, Byung-Jae Choi

Abstract:

It is important for an autonomous mobile robot to know where it is in any time in an indoor environment. In this paper, we design a relative self-localization algorithm. The algorithm compare the interest point in two images and compute the relative displacement and orientation to determent the posture. Firstly, we use the SURF algorithm to extract the interest points of the ceiling. Second, in order to reduce amount of calculation, a replacement SURF is used to extract orientation and description of the interest points. At last, according to the transformation of the interest points in two images, the relative self-localization of the mobile robot will be estimated greatly.

Keywords: Relative Self-Localization Posture, SURF, Natural Landmark, Interest Point.

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755 The Relative Efficiency of Parameter Estimation in Linear Weighted Regression

Authors: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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754 A Zero-Cost Collar Option Applied to Materials Procurement Contracts to Reduce Price Fluctuation Risks in Construction

Authors: H. L. Yim, S. H. Lee, S. K. Yoo, J. J. Kim

Abstract:

This study proposes a materials procurement contracts model to which the zero-cost collar option is applied for heading price fluctuation risks in construction.The material contract model based on the collar option that consists of the call option striking zone of the construction company(the buyer) following the materials price increase andthe put option striking zone of the material vendor(the supplier) following a materials price decrease. This study first determined the call option strike price Xc of the construction company by a simple approach: it uses the predicted profit at the project starting point and then determines the strike price of put option Xp that has an identical option value, which completes the zero-cost material contract.The analysis results indicate that the cost saving of the construction company increased as Xc decreased. This was because the critical level of the steel materials price increasewas set at a low level. However, as Xc decreased, Xpof a put option that had an identical option value gradually increased. Cost saving increased as Xc decreased. However, as Xp gradually increased, the risk of loss from a construction company increased as the steel materials price decreased. Meanwhile, cost saving did not occur for the construction company, because of volatility. This result originated in the zero-cost features of the two-way contract of the collar option. In the case of the regular one-way option, the transaction cost had to be subtracted from the cost saving. The transaction cost originated from an option value that fluctuated with the volatility. That is, the cost saving of the one-way option was affected by the volatility. Meanwhile, even though the collar option with zero transaction cost cut the connection between volatility and cost saving, there was a risk of exercising the put option.

Keywords: Construction materials, Supply chain management, Procurement, Payment, Collar option

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753 Adaptive Neuro-Fuzzy Inference System for Financial Trading using Intraday Seasonality Observation Model

Authors: A. Kablan

Abstract:

The prediction of financial time series is a very complicated process. If the efficient market hypothesis holds, then the predictability of most financial time series would be a rather controversial issue, due to the fact that the current price contains already all available information in the market. This paper extends the Adaptive Neuro Fuzzy Inference System for High Frequency Trading which is an expert system that is capable of using fuzzy reasoning combined with the pattern recognition capability of neural networks to be used in financial forecasting and trading in high frequency. However, in order to eliminate unnecessary input in the training phase a new event based volatility model was proposed. Taking volatility and the scaling laws of financial time series into consideration has brought about the development of the Intraday Seasonality Observation Model. This new model allows the observation of specific events and seasonalities in data and subsequently removes any unnecessary data. This new event based volatility model provides the ANFIS system with more accurate input and has increased the overall performance of the system.

Keywords: Adaptive Neuro-fuzzy Inference system, High Frequency Trading, Intraday Seasonality Observation Model.

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752 Two New Relative Efficiencies of Linear Weighted Regression

Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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