Stochastic models of exchange-rate dynamics and their implications for the pricing of foreign-currency options.

The aim of this study is to find a suitable approach to model econometrically exchange-rate dynamics. In the first chapter, I examine the empirical properties of four exchange rates. The data used are daily, weekly, monthly and quarterly exchange rates of the German mark, the British pound, the Swiss franc, and the Japanese yen against the U.S. dollar from July 1974 to December 1987.1 study the moment properties and time-series properties of these exchange rates and find in daily and weekly data leptokurtosis and heteroskedasticity. On the other hand, the hypotheses of no serial correlation, of a constant mean of zero, and of a symmetric distribution cannot be rejected. The fact that the daily and weekly data are not strictly equi-distant does not have a strong impact on these empirical regularities. In chapter 2, static distributional models (mixture of distributions, compound Poisson process, Student distribution, and stable Paretian distributions) are estimated. Chi-squared goodness-of-fit tests reject these models. Direct inferential evidence against stable distributions is found by estimating the characteristic exponent by FFT and by estimating the exponent of regularly varying tails. In chapter 3, dynamic models of heteroskedasticity (ARCH and Markov-switching models) are introduced. Quite satisfactory results are obtained for the EGARCH model and the Markov-switching model whereas the ARCH, GARCH and GARCH-t models are in conflict with stationarity conditions for the variance. Chapter 4 compares the static and dynamic models with respect to goodness-of-fit and forecasting performance. With respect to goodness-of-fit criteria, the dynamic models appear to be superior to the static models. Furthermore, the dynamic models outperform a naive model of constant variance with respect to unbiasedness but not with respect to precision. Chapter 5 studies the option-price implications of the static and dynamic models. The spot-rate effects of static models are rather small and they disappear, as expected, under temporal aggregation. GARCH and EGARCH models, on the other hand, imply higher option prices compared to Black-Scholes option prices along the whole spectrum of moneyness. Only the Markov-switching model is compatible with observed smile effects

Volatility Model for Financial Market Risk Management : An Analysis on JSX Index Return Covariance Matrix

In measuring risk, practitioners have practiced one of the two extreme approaches for so long, i.e. historical simulation or risk metrics. Meanwhile, academicians tend to apply methods based on the latest development in financial econometrics. In this study, we try to assess one of important issues in financial econometric development that focuses on market risk measurement and management employing asset-based models, i.e. models that apply dimensional covariance matrix, which is relevant to practice world. We compare covariance matrix model with Exponential Smoothing Model and GARCH Derivation and the Associated Derivation Models, using JSX Stock price Index data in 2000-2005. The result of this study shows how applicable the observed financial econometric instrument in Financial Market Risk Management practice.Risk Management, Volatility Model

Modelling and forecasting exchange-rate volatility with ARCH-type models

The statistical analysis of short-run exchange-rate data shows that there is strong heteroskedasticity and serial dependence of volatility. In addition, the empirical distributions are leptokurtic. The model of generalized autoregressive conditional heteroskedasticity (GARCH) seems to be ideally suited to model these empirical regularities because the model incorporates autocorrelated volatility explicity and it also implies a leptokurtic distribution. The GARCH model does indeed achieve a reasonably good fit to the exchange-rate data. However, the GARCH model is not able to outperform the naive forecasts of volatility which use the current estimate of the variance from the past data. --

W-Peakedness: A Simulation based Study

Kurtosis is a commonly used descriptive statistics. Kurtosis “Coefficient of excess” is critically reviewed in different aspects and is called as, measuring the fatness of the tails of the density functions, concentration towards the central value, scattering away from the target point or degree of peakedness of probability distribution. Kurtosis is referred to the shape of the distribution but many distributions having same kurtosis value may have different shapes while Kurtosis may exist when peak of a distribution is not in existence. Through extensive study of kurtosis on several distributions, Wu (2002) introduced a new measure called “W-Peakedness” that offers a fine capture of distribution shape to provide an intuitive measure of peakedness of the distribution which is inversely proportional to the standard deviation of the distribution. In this paper the work is extended for different others continuous probability distributions. Empirical results through simulation illustrate the proposed method to evaluate kurtosis by W-peakednes

Three essays on modeling stock returns: empirical analysis of the residual distribution, risk-return relation, and stock-bond dynamic correlation

This dissertation studies the following issues: the presence of non-normal distribution features and the significance of higher order moments, the tradeoff between risk and return, and the dynamic conditional correlation between stock returns and bond returns. These issues are structured into three essays.Essay #1 tackles the non-normal features by employing the exponential generalized beta distribution of the second kind (EGB2) to model 30 Dow Jones industrial stock returns. The evidence suggests that the model with the EGB2 distribution assumption is capable of taking care of stock return characteristics, including fat tails, peakedness (leptokurtosis), skewness, clustered conditional variance, and leverage effect, therefore, is capable of making a good prediction on the happenings of extreme values. The goodness of fit statistic provides supporting evidence in favor of the EGB2 distribution in modeling stock returns. Evidence also suggests that the leverage effect is diminished when higher order moments are considered.Essay #2 examines the risk-return relation by applying high frequency data of 30 Dow Jones industrial stocks. I find some supportive evidence in favor of the positive relation between the expected excess return and expected risk. However, this positive relation is not revealed for all 30 stocks using a standard weighted least squares regression (WLS) method. Using a quantile regression method, I find that the risk-return relation evolves from negative to positive as the returns’ quantile increases. This essay also finds interesting evidence that the intraday skewness coefficient explains a great deal of the variation in the excess returns.Essay #3 mainly focuses on the analysis of the time-varying correlations between stock and bond returns using the asymmetric dynamic conditional correlation (ADCC) model (Cappiello et al., 2004). The estimated coefficients show some volatile behavior and display some degree of persistence over time. Testing the asymmetric dynamic correlations by using a set of macroeconomic information, I find that the federal funds rate, the relative volatility between the stock and bond markets, the yield spread, and oil price shocks are the significant factors for the coefficients’ time varying.Ph.D., Finance -- Drexel University, 200

Volatility and the Euro: an Irish perspective

With Ireland joining the Euro, exchange rate risk between participating states is gone. However, as is known, this new currency will continue to face exchange rate risk, and the general reduction of volatility on a day to day basis for Irish economic agents neglects to take account of possible extreme problems with the Euro. In this paper we will see that even though the Euro is a managed (irrevocably fixed) system, trade between Ireland and non-members, most notably the US, involves two separate currencies. This trade will require currency trading, leading to the possibility of large downside exposure to exchange rate risk for Irish exporters. In order to determine the extent to which the currencies can fluctuate, this paper examines exchange rate volatility using an Extreme Value approach. A number of different volatility scenarios are offered based on extrapolation of different exchange rate regimes under two broad headings, floating and managed. Using these headings, a number of actual systems are analysed including the ERM, the Snake in the Tunnel and Bretton Woods.

Semi-moments based tests of normality and the evolution of stock returns towards normality.

Testing for normality is of paramount importance in many areas of science since the Gaussian distribution is a key hypothesis in many models. As the use of semi–moments is increasing in physics, economics or finance, often to judge the distributional properties of a given sample, we propose a test of normality relying on such statistics. This test is proposed in three different versions and an extensive study of their power against various alternatives is conducted in comparison with a number of powerful classical tests of normality. We find that semi–moments based tests have high power against leptokurtic and asymmetric alternatives. This new test is then applied to stock returns, to study the evolution of their normality over different horizons. They are found to converge at a “log-log” speed, as are moments and most semi–moments. Moreover, the distribution does not appear to converge to a real Gaussian.Stock returns; Volatility (finance); Gaussian;

New Technique to Estimate the Asymmetric Trimming Mean

A trimming mean eliminates the extreme observations by removing observations from each end of the ordered sample. In this paper, we adopted the Hogg's and Brys's tail weight measures. In addition, a new algorithm was proposed as a linear estimator based on the quartile; we used a quartile to divide the data into three and four groups. Then two new estimators were proposed. These classes of linear estimators were examined via simulation method over a variety of asymmetric distributions. Sample sizes 50, 100, 150, and 200 were generated using R program. The results of 50 were tabulated, since we have similar results for the other sizes. These results were tabulated for 7 asymmetric distributions with total trimmed proportions 0.10 and 0.20 on both sides, respectively. The results for these estimators were ordered based on their relative efficiency