Stavros Degiannakis

ARCH models for financial applications

ARCH models for the daily S&P500 log-returns are estimated, whereas the intraday prices comprise the dataset for an ARFIMAX model. Model’s forecasting performance is statistically superior when the CBOE’s VIX index is incorporated as an explanatory variable.

Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

Abstract Autoregressive Conditional Heteroscedasticity (ARCH) models have successfully been employed in order to predict asset return volatility. Predicting volatility is of great importance in pricing financial derivatives, selecting portfolios, measuring and managing investment risk more accurately. In this paper, a number of univariate and multivariate ARCH models, their estimating methods and the characteristics of financial time series, which are captured by volatility models, are presented. The number of possible conditional volatility formulations is vast. Therefore, a systematic presentation of the models that have been considered in the ARCH literature can be useful in guiding one’s choice of a model for exploiting future volatility, with applications in financial markets.

Modeling risk for long and short trading positions

Purpose – Aims to investigate the accuracy of parametric, nonparametric, and semiparametric methods in predicting the one-day-ahead value-at-risk (VaR) measure in three types of markets (stock exchanges, commodities, and exchange rates), both for long and short trading positions. Design/methodology/approach – The risk management techniques are designed to capture the main characteristics of asset returns, such as leptokurtosis and asymmetric distribution, volatility clustering, asymmetric relationship between stock returns and conditional variance, and power transformation of conditional variance. Findings – Based on back-testing measures and a loss function evaluation method, finds that the modeling of the main characteristics of asset returns produces the most accurate VaR forecasts. Especially for the high confidence levels, a risk manager must employ different volatility techniques in order to forecast accurately the VaR for the two trading positions. Practical implications – Different models achieve accurate VaR forecasts for long and short trading positions, indicating to portfolio managers the significance of modeling separately the left and the right side of the distribution of returns. Originality/value – The behavior of the risk management techniques is examined for both long and short VaR trading positions; to the best of ones knowledge, this is the first study that investigates the risk characteristics of three different financial markets simultaneously. Moreover, a two-stage model selection is implemented in contrast with the most commonly used back-testing procedures to identify a unique model. Finally, parametric, nonparametric, and semiparametric techniques are employed to investigate their performance in a unified environment.

Evaluating volatility forecasts in option pricing in the context of a simulated options market

The performance of an ARCH model selection algorithm based on the standardized prediction error criterion (SPEC) is evaluated. The evaluation of the algorithm is performed by comparing different volatility forecasts in option pricing through the simulation of an options market. Traders employing the SPEC model selection algorithm use the model with the lowest sum of squared standardized one-step-ahead prediction errors for obtaining their volatility forecast. The cumulative profits of the participants in pricing 1-day index straddle options always using variance forecasts obtained by GARCH, EGARCH and TARCH models are compared to those made by the participants using variance forecasts obtained by models suggested by the SPEC algorithm. The straddles are priced on the Standard and Poor 500 (S & P 500) index. It is concluded that traders, who base their selection of an ARCH model on the SPEC algorithm, achieve higher profits than those, who use only a single ARCH model. Moreover, the SPEC algorithm is compared with other criteria of model selection that measure the ability of the ARCH models to forecast the realized intra-day volatility. In this case too, the SPEC algorithm users achieve the highest returns. Thus, the SPEC model selection method appears to be a useful tool in selecting the appropriate model for estimating future volatility in pricing derivatives.

Backtesting VaR models:a two-stage procedure

Academics and practitioners have extensively studied Value-at-Risk (VaR) to propose a unique risk management technique that generates accurate VaR estimations for long and short trading positions. However, they have not succeeded yet as the developed testing frameworks have not been widely accepted. A two-stage backtesting procedure is proposed in order a model that not only forecasts VaR but also predicts the loss beyond VaR to be selected. Numerous conditional volatility models that capture the main characteristics of asset returns (asymmetric and leptokurtic unconditional distribution of returns, power transformation and fractional integration of the conditional variance) under four distributional assumptions (normal, GED, Student-t, and skewed Student-t) have been estimated to find the best model for three financial markets (US stock, gold and dollar-pound exchange rate markets), long and short trading positions, and two confidence levels. By following this procedure, the risk manager can significantly reduce the number of competing models.

ARFIMAX and ARFIMAX-TARCH realized volatility modeling

ARFIMAX models are applied in estimating the intra-day realized volatility of the CAC40 and DAX30 indices. Volatility clustering and asymmetry characterize the logarithmic realized volatility of both the indices. The ARFIMAX model with time-varying conditional heteroskedasticity is the best performing specification and, at least in the case of DAX30, provides statistically superior next trading days realized volatility forecasts.

Evaluating value-at-risk models before and after the financial crisis of 2008: International evidence

Purpose - The purpose of this paper is to focus on the performance of three alternative value-at-risk (VaR) models to provide suitable estimates for measuring and forecasting market risk. The data sample consists of five international developed and emerging stock market indices over the time period from 2004 to 2008. The main research question is related to the performance of widely-accepted and simplified approaches to estimate VaR before and after the financial crisis. Design/methodology/approach - VaR is estimated using daily data from the UK (FTSE 100), Germany (DAX30), the USA (SP classic GARCH(1,1) model of conditional variance assuming a conditional normally distributed returns; and asymmetric GARCH with skewed Student- Findings - The paper provides evidence that the tools of quantitative finance may achieve their objective. The results indicate that the widely accepted and simplified ARCH framework seems to provide satisfactory forecasts of VaR, not only for the pre-2008 period of the financial crisis but also for the period of high volatility of stock market returns. Thus, the blame for financial crisis should not be cast upon quantitative techniques, used to measure and forecast market risk, alone. Practical implications - Knowledge of modern risk management techniques is required to resolve the next financial crisis. The next crisis can be avoided only when financial risk managers acquire the necessary quantitative skills to measure uncertainty and understand risk. Originality/value - The main contribution of this paper is that it provides evidence that widely accepted/used methods give reliable VaR estimates and forecasts for periods of financial turbulence (financial crises).

Forecasting one‐day‐ahead VaR and intra‐day realized volatility in the Athens Stock Exchange Market

Purpose - The aim is to evaluate the performance of symmetric and asymmetric ARCH models in forecasting both the one-day-ahead Value-at-Risk (VaR) and the realized intra-day volatility of two equity indices in the Athens Stock Exchange. Design/methodology/approach - Two volatility specifications are estimated, the symmetric generalized autoregressive conditional heteroscedasticity (GARCH) and the asymmetric APARCH processes. The data set consisted of daily closing prices of the General and the Bank indices from 25 April 1994 to 19 December 2003 and their intra day quotation data from 8 May 2002 to 19 December 2003. Findings - Under the VaR framework, the most appropriate method for the Bank index is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one-step-ahead intra-day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index. Originality/value - As concerns the Greek stock market, there are adequate methods in predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.

Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models

A number of ARCH models are considered in the framework of evaluating the performance of a method for model selection based on a standardized prediction error criterion (SPEC). According to this method, the ARCH model with the lowest sum of squared standardized forecasting errors is selected for predicting future volatility. A number of statistical criteria, that measure the distance between predicted and inter-day realized volatility, are used to examine the performance of a model to predict future volatility, for forecasting horizons ranging from one day to 100 days ahead. The results reveal that the SPEC model selection procedure has a satisfactory performance in picking that model that generates ‘better’ volatility predictions. A comparison of the SPEC algorithm with a set of other model evaluation criteria yields similar findings. It appears, therefore, that it can be regarded as a tool in guiding the choice of the appropriate model for predicting future volatility, with applications in evaluating portfolios, managing financial risk and creating speculative strategies with options.

Rolling-sampled parameters of ARCH and Levy-stable models

In this article an asymmetric autoregressive conditional heteroskedasticity (ARCH) model is applied to some well-known financial indices (DAX30, FTSE20, FTSE100 and SP500), using a rolling sample of constant size, in order to investigate whether the values of the estimated parameters of the model change over time. Although, there are changes in the estimated parameters reflecting that structural properties and trading behaviour alter over time, the ARCH model adequately forecasts the one-day-ahead volatility. A simulation study has been carried out to investigate whether the time-variant attitude holds in the case of a generated ARCH data process revealing that either in that case the rolling-sampled parameters are time varying. The rolling analysis is also applied to estimate the parameters of a Levy-stable distribution. The empirical findings support that the stable parameters are also time variant.