The Martingale Restriction and Relative Market Efficiency between KOSPI 200 Index and Index Options Market

This paper examines the martingale restriction for the KOSPI 200 index options market. And in cases of the rejections, we investigate the relative market efficiency between stock index and stock index options market, using approximate entropy (ApEn) method proposed by Pincus (1994), which quantifies a complexity, irregularity and unpredictability in time series. The empirical results of this study clearly reject the martingale restriction and regression analyses indicate that the historical returns of underlying index can explain about 25% of the price differences between option-implied and market index prices but the total trading volume can explain only a small portion of the price differences. These results have cast doubt on the informational efficiency of this market. Comparing the relative market efficiency based on ApEn have showed that the complexity or irregularity of KOSPI 200 index is larger than the index options during the entire sample period. But, Examining separately ApEn of the magnitude and the sign time series which compose log-returns document that stock index options market reflect more efficiently the information about the direction of price changes than the stock index market in 2014 and the efficiency of the index options market about the directional information may be affected by directional traders who prefer certain strategies designed by exploiting past stock market movements.