Proposals have been made for some stock exchanges to reduce the size of their trading tick in order to lower transactions costs and, as a result, attract more trading volume and firm listings. We investigate the impact of tick size on price clustering and trading volume when the minimum price change varies with price level. Controlling the firm specific variables, we find that a smaller trading tick tends to exacerbate price clustering. Furthermore, a reduction in tick size is more likely to increase trading volume if the shares are heavily traded. These results suggest that previous studies on other stock markets may have overstated the benefits of a smaller trading tick to traders. Copyright Blackwell Publishers Ltd 1998.

The hedging problem is examined where futures prices obey the cost-ofcarry model. The resultant hedging model explicitly incorporates maturity effects in the futures basis. Formulas for the optimal static and dynamic hedges are derived. Although these formulas are developed for the case of direct hedging, the framework used is sufficiently flexible so that these formulas can be applied to many cross-hedging situations. The performance of the model is compared with that of several other models for two hedging scenarios: one involving a financial asset and the other involving a commodity. In both cases, significant maturity effects were found in the first and second moments of the futures basis. Our hedging formulas outperformed other hedging strategies on an ex-ante basis.

The correlation structure of asset returns is a crucial parameter in risk management as well as in theoretical finance. In practice, however, the true correlation structure between the returns of assets can easily become obscured by time variation in the observed correlation structure and in the liquidity of the assets. We employed a timestamped high-frequency data set of exchange rates, namely, the US$-deutsche mark and the US$-yen exchange rates, to calibrate the observed time variation in the correlation structure between theirThe authors would like to thank an anonymous referee and the editor, Robert Webb, for their suggestions and recommendations. returns. We also documented time variation in the liquidity structure of these rates. We then attempted to link the observed correlations with the liquidity via an application of an illiquid trading model first developed by Scholes and Williams (1976). We show that the observed correlation structure is strongly biased by the liquidity and that it is possible to effect at least a partial rectification of the otherwise downward-biased observed correlation. The rectified sample correlation is, therefore, more appropriate for input into models used for forecasting, option pricing, and other risk management applications.

The issue of multiple series of stock purchase warrants by the same firm is an interesting financial structure not just in America, but is common in some countries such as Switzerland, Malaysia, and Singapore. This paper derives valuation formulas for multiple series of outstanding warrants. The theoretical warrant prices from this model are compared against existing models. We report a subtle slippage effect and also a cross dilution effect that cause the existing models such as Galai-Schneller model to be inappropriate for pricing such classes of multiple warrants. We also provide an example to illustrate the practicality of our model. The Greeks of the model are also derived in this paper. The complexity of the multiple warrants could extend to other classes of contingent securities issued by the same firm but with differing expiry terms.

It is widely believed that the conventional futures hedge ratio, is variance-minimizing when it is computed using percentage returns or log returns. It is shown that the conventional hedge ratio is variance-minimizing when computed from returns measured in dollar terms but not from returns measured in percentage or log terms. Formulas for the minimumvariance hedge ratio under percentage and log returns are derived. The difference between the conventional hedge ratio computed from percentage and log returns and the minimum-variance hedge ratio is found to be relatively small when directly hedging, especially when using near-maturity futures. However, the minimum-variance hedge ratio can vary significantly from the conventional hedge ratio computed from percentage or log returns when used in cross-hedging situations. Simulation analysis shows that the incorrect application of the conventional hedge ratio in crosshedging situations can substantially reduce hedging performance.