تجزیه و تحلیل تجربی از کشف قیمت و جانبداری قیمت گذاری در شاخص سهام 200 بازار مشتقات KOSPI

In this paper, Korean financial markets are investigated in two ways, time series and cross-sectional data analysis for the study of market microstructure of price discovery and pricing bias associated with stock index, futures and options. First, the lead–lag relationships among the KOSPI 200 stock index, the index futures, and the index options markets are explored based on minute-to-minute price data. The results explain that the KOSPI 200 stock index futures lead the index, as reported in the previous studies, and the at-the-money options lead the stock index. A symmetric lead–lag relationship is found between futures and options, except for out-of-the-money options. This paper also investigates the consistency of lead–lag relationships among the results from the different time intervals of price data. Second, the causes of the pricing bias in the index options market are analyzed. The pricing bias between the observed KOSPI stock index and implied stock index from at-the-money options are affected by market inefficiency, moneyness, and implied volatility. Time to maturity and trading volumes of call options also affect the pricing bias, while those of put options are not significant.

When new information is released in an efficient and perfect capital market bias, prices of securities and their derivatives fully and instantaneously reflect all available relevant information. But in real markets, there exist market frictions including various transaction costs and information asymmetry in real markets and the lead–lag relationship between markets is observed. It is also observed that the trading costs of security markets and those of derivatives markets are different from each other. This asymmetry in trading costs makes the market with lower trading costs reflect new information more quickly. Because many traders take positions in inter-markets simultaneously, the difference of reaction times and the size of the difference of cross-sectional prices between markets can make a crucial effect on the profits. For this reason, it is of interest to both academics and practitioners to suggest the price discovery process and pricing bias between markets by investigating the lead–lag effects for the price dynamics between markets. Numerous studies have examined the intraday price relationship between the stock index and its derivatives. Kawaller, Koch, and Koch (1987) investigate the intraday price relationship between S&P 500 futures and the S&P 500 index using three-stage least-squares regression. They find that the futures price movements consistently lead index movements by 20 to 45 min on a minute-to-minute data basis, while the index price rarely affects the futures price beyond 1 min. Stoll and Whaley (1990) examine the time series properties of intraday returns of the stock index and stock index futures contracts with 5-min rate of return series of the S&P 500 and major market indexes (MMI) using an ARMA(2, 3) process to purge the effects of infrequent trading. They report that the S&P 500 and MMI futures returns lead stock index returns by about 5 min on average after eliminating infrequent trading and bid/ask price effects. Chan (1992) explores the intraday lead–lag relationship between returns of the MMI and S&P 500 futures using 5-min trading data. He confirms that the S&P futures strongly lead the cash index and suggests that nonsynchronous trading cannot completely explain the lead–lag relationship of futures prices and the cash index. Manaster and Rendleman (1982), Bhattacharya (1987), and Anthony (1988) provide evidence that the options price leads the stock market. Finucane (1991) also reports that the measure of the relative index options price leads the stock market by at least 15 min. But, Stephan and Whaley (1990) document that price changes in the stock market lead price changes in the options market for active CBOE call options about 15 to 20 min on average with a 5-min option price series. Using a nonlinear multivariate regression model, Chan, Chung, and Johnson (1993) confirm Stephan and Whaley's results that stocks lead options by 15 min. They argue that the lead can be caused by the relatively larger option tick, and it might be a spurious lead induced by infrequent trading of options. Abhyankar (1995) reports that the FTSE 100 index futures market leads by up to 1 h using hourly data for the FTSE 100 cash and futures markets. Fleming, Ostdiek, and Whaley (1996) provide a trading cost hypothesis for the relative rates of price discovery in the stock index, futures, and options markets. Their empirical results with 5-min returns for the markets show that S&P 500 index futures lead the S&P 500 stock index, and S&P 100 index options lead the S&P 100 stock index, even after controlling for the effects of infrequent trading on the indexes. Gwilym and Buckle (2001) also examine the lead–lag relationships between the FTSE 100 stock index and its derivatives markets with hourly data. They report that the index call options strongly lead the index futures, and the futures strongly lead puts, which suggest that expectations of rises or falls in the market may affect the lead–lag relationship between markets. The purpose of this article is to provide the price discovery functions of KOSPI 200 stock index options related to the stock index and the futures market based on minute-to-minute price data. Because of the trading volume problem, there have been few studies that deal with the lead–lag relationships among the three markets based on minute-to-minute data. The primary elements affecting pricing bias of the options market to the observed stock index are also analyzed using the multiple regression model. The KOSPI 200 stock index futures and options are one of the biggest financial markets, and they have ranked first in the world in terms of the trading volume since 1999. In 2003, the combined trading volume reached 2.9 billion contracts which accounted for a 37.2% share of total contracts in the world. The sufficient liquidity of the markets ensures that the KOSPI 200 stock index futures and options markets are appropriate for the study of market microstructure of price discovery and pricing bias associated with stock index, futures and options markets. This article is organized as follows. In Section 2, the description of the data is given. All tests are based on minute-to-minute intraday prices of the KOSPI 200 stock index, the index futures and the index options. Section 3 explains the methodology in this study and Section 4 explores the lead–lag relationship among the markets, and the pricing bias factors between the index market and the index options market. Summary and conclusions are presented in Section 5.

This article investigates the price discovery function with the lead–lag relationship for the KOSPI 200 stock index, futures and options over 2 years and 3 months, from May 2001 to June 2003. The results show that the KOSPI 200 stock index futures lead the KOSPI 200 stock index by 23 min as reported in the previous studies. The stock index lags the at-the-money call options and at-the-money put options by 9 and 5 min respectively. The lead–lag relationship between the index and the futures markets is similar to that between the index and in-the-money (or out-of-the-money) options or the futures and in-the-money (or out-of-the-money) options. A symmetric lead–lag relationship has been found between the futures and the options except out-of-the-money options. This results support the trading cost hypothesis suggested by Fleming et al. (1996) which argue that the derivative markets give the investors much lower trading costs than the stock index markets. Besides, the lead–lag relationships between the markets are in accordance with the leverage effect hypothesis arguing that the derivatives markets should lead the stock index markets. Informed traders in the KOSPI 200 stock index and its derivatives markets may react faster to stock index derivatives markets than the stock index markets because of the leverage effect and lower transaction costs. This can be supported by the trading volume. In particular, the sufficient trading volume in the deep-in-the-money options provides strong evidence for the proposition. The infrequent trading effect can be found in the (deep) in-the-money options. The relatively larger option tick appears to prevent investors from taking arbitrage chances with in-the-money options. Moreover, the out-of-the-money options are quite appropriate for maximizing the profits for the volatility-based traders. These lead a relatively small liquidity of the in-the-money options and they are deprived of flexibility in price changes. For this reason the (deep)-out-of-the-money options with sufficient liquidity are more adequate for analyzing the price discovery function for the stock index or index futures markets. Finally, this article explores the causes for the pricing bias between the observed KOSPI stock index and implied stock index from at-the-money options. The effects on pricing bias of market inefficiency, moneyness, time to maturity, volatility, and trading volume have been examined. The results show that as options are farther than at-the-money, and as implied volatility increases, pricing bias expands as well. As the market inefficiency increases, pricing bias is decreased in call options, however, pricing bias is increased in put options. Time to maturity and trading volumes of call options are important determinants for expanding the pricing bias, while the coefficients of time to maturity and trading volumes of put options are not significant.