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. --

Forecasting volatility and option pricing for exchange-rate dynamics: a comparison of models

This paper explores the applicability of static and dynamic models to capture the stylized facts of exchange-rate dynamics. The static models (mixture of distributions, compound Poisson process, generalized Student distribution) are compatible with leptokurtosis and can be characterized as scale-compounded distributions. The dynamic models (GARCH, GARCH-t, EGARCH, Markov-switching model), on the other hand, are compatible with both leptokurtosis and heteroskedasticity. In a comparison of the candidate models, it is found that the dynamic models do indeed achieve a better fit to the data than the static models. However, in forecasting experiments the dynamic models can outperform a 'naive' model of constant variances only with respect to unbiasedness but not with respect to precision. Furthermore, the paper examines the implications of the static and dynamic models for the pricing of foreign-currency options by simple simulations. Static models show significang option-price effect only when the maturity is short. GARCH and EGARCH models, on the other hand, imply options prices which are higher than Black-Scholes prices for the full range of moneyness. Only the Markov-switching model is compatible with the observed 'smile effects' on option markets. --

On the modelling of speculative prices by stable Paretian distributions and regularly varying tails

Earlier studies which applied the family of stable Paretian distributions to financial data are inconclusive and contradictory. In this article I estimate the parameters of the model by the Feuerverger-McDunnough method which enables the application of maximum likelihood rhethods. Based on inferential statistics, stable Paretian distributions can be rejected with monthly data. In order to confirm this result, the model is extended to the family of distributions with regularly varying tails. The result that stable Paretian distributions are not applicable is indeed confirmed by estimating the coefficient of regular variation. --

Fischer Decomposition for Difference Dirac Operators

We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a Fischer decomposition for the discrete Laplacian

Light hadronic physics using domain wall fermions in quenched lattice QCD

In the past year domain wall fermion simulations have moved from exploratory stages to the point where systematic effects can be studied with different gauge couplings, volumes, and lengths in the fifth dimension. Results are presented here for the chiral condensate, the light hadron spectrum, and the strange quark mass. We focus especially on the pseudoscalar meson mass and show that, in small volume, the correlators used to compute it can be contaminated to different degrees by topological zero modes. In large volume a nonlinear extrapolation to the chiral limit, e.g. as expected from quenched chiral perturbation theory, is needed in order to have a consistent picture of low energy chiral symmetry breaking effects.Comment: To appear in the proceedings of Lattice 2000 (spectrum), Bangalore, India. Work done as part of the RIKEN/BNL/Columbia Collaboration. (4 pages) - Reference adde

Markov-switching models for exchange-rate dynamics and the pricing of foreign-currency options

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Delta-neutral volatility trading with intra-day prices: an application to options on the DAX

This paper evaluates the profitability of applying four different volatility forecasting models to the trading of straddles on the German stock market index DAX. Special care has been taken to use simultaneous intra-day prices and realistic transaction costs. Furthermore, straddle positions were evaluated on a daily basis to preserve delta neutrality. The four models applied in this paper are: historical volatility, two ARCH models, and an autoregressive model for the volatility index. VDAX. The ARCH models perform best in generating profits for market makers. Forecasts based on historical volatility also produce statistically and economically significant profits over the two-year simulation period of 1993 and 1994. In general, a filter1rule with a small filter of0.5 per cent produces the best results for both the ARCH models and historical volatility. However, the VDAX-AR model generates much lower and usually insignificant profits, and for some filter rules this model even has cumulative losses for market makers. For non-market-makers and non-members of exchange, however, larger transaction\costs imply that no significant profits can be gained with any model of volatility forecasts. --