A measurement of the extent of market imperfections between markets and applications

Abstract

Traditionally, market imperfections are measured separately. In dealing with the impacts of market imperfections on a financial theory, financial researchers often modify the theory by incorporating one type of market imperfections into the theory, one by one, and then derive a new modified formula. The major problem with this approach is that when considering a type of market imperfections, the new modified formula still ignores the effects of other types of market imperfections. Another problem is that the modified formula is often tedious. Following the concept of degree of market imperfection in Hsu and Wang (2004), this article aims to derive a more easy measurement of market imperfections between markets, discuss some useful applications and provide one of empirical tests. The degree of market imperfection between markets can be applied at least to the following areas: (1) theoretical model building for pricing derivatives in imperfect markets, (2) predicting the deviations of the actual derivative prices from their theoretical prices based on the model of perfect market assumptions and (3) showing the extent of arbitrage activities between markets.

Acknowledgements

The authors would like to thank the Editor, Professor Mark Taylor, and Associate Editor for their extremely helpful comments. The financial support from the National Science Council, Taiwan, is very appreciated (NSC-94-2416-H-165-002).

Notes

¹ A hedged portfolio can be formed by taking, for example, a short position in futures (or options) and a long position in the underlying asset, and then rebalancing the two positions continuously.

² See Introduction section.

³ For the detailed derivation of this solution, see Hsu and Wang (2004), Appendix, pp. 179–82.

⁴ The reason that we only demonstrate the second application is that the first application has already been shown in Hsu and Wang (2004), and the third application is no more than a practical application.

⁵ In results not reported here, we repeat our tests using the exponentially weighted moving average method and find that the results are similar to those of the equally weighted moving average method.

⁶ If the underlying stock index pays a continuous, constant dividend yield, the cost of carry model is: F_t = S_te ^{( r – q )( T – t )}, where F_t is the theoretical futures price, S_t denotes the current stock index, r is the risk-free rate, q is the dividend yield, and T − t denotes the time to expiration. If the underlying stock index pays irregular lumpiness of dividends, the cost of carry model is where D_t is the sum of the present values of all cash dividends distributed by the underlying component stocks at time t; d_i is the cash dividend per share for stock i; w_i is the weight of stock i in the index; t_i is the time that stock i pays the cash dividend; and p_{i , t} is the price of stock i at time t.

⁷ See footnote 6.