Long Memory Persistence in the Factor of Implied Volatility Dynamics

The volatility implied by observed market prices as a function of the strike and time to maturity form an Implied Volatility Surface (IV S). Practical applications require reducing the dimension and characterize its dynamics through a small number of factors. Such dimension reduction is summarized by a Dynamic Semiparametric Factor Model (DSFM) that characterizes the IV S itself and their movements across time by a multivariate time series of factor loadings. This paper focuses on investigating long range dependence in the factor loadings series. Our result reveals that shocks to volatility persist for a very long time, affecting significantly stock prices. For appropriate representation of the series dynamics and the possibility of improved forecasting, we model the long memory in levels and absolute returns using the class of fractional integrated volatility models that provide flexible structure to capture the slow decaying autocorrelation function reasonably well.Implied Volatility, Dynamic Semiparametric Factor Modeling, Long Memory, Fractional Integrated Volatility Models.

Value-at-Risk and Expected Shortfall when there is long range dependence.

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and forecasting of market volatility. The implication is that models that accomodate long memory hold the promise of improved long-run volatility forecast as well as accurate pricing of long-term contracts. On the other hand, recent focus is on whether long memory can affect the measurement of market risk in the context of Value-at- Risk (V aR). In this paper, we evaluate the Value-at-Risk (V aR) and Expected Shortfall (ESF) in financial markets under such conditions. We examine one equity portfolio, the British FTSE100 and three stocks of the German DAX index portfolio (Bayer, Siemens and Volkswagen). Classical V aR estimation methodology such as exponential moving average (EMA) as well as extension to cases where long memory is an inherent characteristics of the system are investigated. In particular, we estimate two long memory models, the Fractional Integrated Asymmetric Power-ARCH and the Hyperbolic-GARCH with different error distribution assumptions. Our results show that models that account for asymmetries in the volatility specifications as well as fractional integrated parametrization of the volatility process, perform better in predicting the one-step as well as five-step ahead V aR and ESF for short and long positions than short memory models. This suggests that for proper risk valuation of options, the degree of persistence should be investigated and appropriate models that incorporate the existence of such characteristic be taken into account.Backtesting, Value-at-Risk, Expected Shortfall, Long Memory, Fractional Integrated Volatility Models

On the Difficulty to Design Arabic E-learning System in Statistics

In this paper, we present a case study, which describe the development of the Statistic e-learning-course in Arabic language –``Arabic MM*STAT´´. The basic frame forthis E-book, the system MM*STAT was developed at the School for Business and Economics of Humboldt-Universität zu Berlin. Arabic MM*STAT uses a HTML - based filing card structure. We discuss the difficulties of the implementation of such a system in to the standard WWW formats and present the solutions needed for Arab educational institutions and the Arabic user. Those solutions are consistent with the Arabic language, and include the modern trend in the e-learning environment.electronic books, Arabtex, MM*STAT, Statistical software

A Joint Analysis of the KOSPI 200 Option and ODAX Option Markets Dynamics

As a function of strike and time to maturity the implied volatility estimation is a challenging task in nancial econometrics. Dynamic Semiparametric Factor Models (DSFM) are a model class that allows for the estimation of the implied volatility surface (IVS) in a dynamic context, employing semiparametric factor functions and time-varying loadings. Because nancial asset volatilities move over time, across assets and over markets, this paper analyses volatility interaction between German and Korean stock markets. As proxy for the volatility, factor loadings series derived from a DSFM application on option prices are employed. We examine volatility transmission between the markets under the vector autoregressive (VAR) model framework. Our results show that a shock in the volatility of one market may not translate directly into greater uncertainty in another market and it is unlikely that portfolio investors can benet from diversication among these markets due to cointegration.implied volatility surface, dynamic semiparametric factor model, VAR, cointegration

VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings

The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading times series using the vector autoregressive (VAR) framework and analyzes associated movements of these factors with movements in some macroeconomic variables of the Euro - economy.Implied volatility surface, dynamic semiparametric factor model, unit root tests, vector autoregression, impulse responses

e-learning/e-teaching

In today’s net-based technology culture, a new way of learning/teaching, accessing or preparing learning materials is finding root in Education. It is enabling individuals and institutions to play a more powerful and attractive role in the education process, referred to as e-learning. E-learning is internet-enabled learning that uses net work technology to design, deliver, select, administer and extend learning. Though there are observable increase for multimedia education in various subject fields, the e-learning/e-teaching of statistics and its application to some subject areas is lacking. Statistics as the science of obtaining, processing, and interpreting information from highly complex structural data is often difficult for learners. It requires skills in handling quantitative, graphical as well as mathematical ability. Developing e-learning/e-teaching tool to address these concerns is a powerful and attractive way in which statistics and its application will benefit from e-learning. This thesis is based on such a tool, the MD*Book. It constitute two sections, - Chapters 1 to 4: Introduces e-learning/e-teaching concept, the MD*Book tool and the XploRe Quantlet Client (XQC) techniques. I exemplify the application of MD*Book: e-learning/e-teaching with an implementation to a Finance Introductory Course, FIC MD*Booklet. The implementation herein is a reflection of one of the several enhanced examples on statistical methods and analysis in course content using the XploRe quantlet technology. - Chapters 5 to 6: Explores criteria for e-learning evaluation, investigates e-learning/e-teaching with FIC MD*Booklet through an evaluation study on its learning innovation and outline some suggestions and remarks on the findings. Chapter 7 presents a conclusion on the project in this thesis

Long Memory Persistence in the Factor of ImpliedVolatility Dynamics

The volatility implied by observed market prices as a function of the strike and time to maturity form an Implied Volatility Surface (IV S). Practical applications require reducing the dimension and characterize its dynamics through a small number of factors. Such dimension reduction is summarized by a Dynamic Semiparametric Factor Model (DSFM) that characterizes the IV S itself and their movements across time by a multivariate time series of factor loadings. This paper focuses on investigating long range dependence in the factor loadings series. Our result reveals that shocks to volatility persist for a very long time, affecting significantly stock prices. For appropriate representation of the series dynamics and the possibility of improved forecasting, we model the long memory in levels and absolute returns using the class of fractional integrated volatility models that provide flexible structure to capture the slow decaying autocorrelation function reasonably well

Value-at-Risk and Expected Shortfall when there is long range dependence

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and forecasting of market volatility. The implication is that models that accomodate long memory hold the promise of improved long-run volatility forecast as well as accurate pricing of long-term contracts. On the other hand, recent focus is on whether long memory can affect the measurement of market risk in the context of Value-at- Risk (V aR). In this paper, we evaluate the Value-at-Risk (V aR) and Expected Shortfall (ESF) in financial markets under such conditions. We examine one equity portfolio, the British FTSE100 and three stocks of the German DAX index portfolio (Bayer, Siemens and Volkswagen). Classical V aR estimation methodology such as exponential moving average (EMA) as well as extension to cases where long memory is an inherent characteristics of the system are investigated. In particular, we estimate two long memory models, the Fractional Integrated Asymmetric Power-ARCH and the Hyperbolic-GARCH with different error distribution assumptions. Our results show that models that account for asymmetries in the volatility specifications as well as fractional integrated parametrization of the volatility process, perform better in predicting the one-step as well as five-step ahead V aR and ESF for short and long positions than short memory models. This suggests that for proper risk valuation of options, the degree of persistence should be investigated and appropriate models that incorporate the existence of such characteristic be taken into account

A Joint Analysis of the KOSPI 200 Option and ODAX Option Markets Dynamics

As a function of strike and time to maturity the implied volatility estimation is a challenging task in financial econometrics. Dynamic Semiparametric Factor Models (DSFM) are a model class that allows for the estimation of the implied volatility surface (IVS) in a dynamic context, employing semiparametric factor functions and time-varying loadings. Because financial asset volatilities move over time, across assets and over markets, this paper analyses volatility interaction between German and Korean stock markets. As proxy for the volatility, factor loadings series derived from a DSFM application on option prices are employed. We examine volatility transmission between the markets under the vector autoregressive (VAR) model framework. Our results show that a shock in the volatility of one market may not translate directly into greater uncertainty in another market and it is unlikely that portfolio investors can benefit from diversification among these markets due to cointegration

VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings

The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric modelsapproximate the implied volatility surface (IVS) in a finite dimensional function space,allowing for a low dimensional factor representation of these dynamics. This paperpresents an investigation into the stochastic properties of the factor loading times seriesusing the vector autoregressive (VAR) framework and analyzes associated movements of these factors with movements in some macroeconomic variables of the Euro-economy