# Information spillovers between stock and options markets

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<ul><li> 1. Information spillover effects between stock and option markets Fredrik Berchtold and Lars Nordn1 School of Business, Stockholm University, S-106 91 Stockholm, Sweden. Abstract This study analyses information spillover effects between the Swedish OMX stock index and the index option market. Two types of information are analysed in a bivariate Vectorized Autoregressive (VAR) setup with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) errors. The first type represents information where an informed investor knows whether the stock index will increase or decrease. The second type is less specific, the direction is unknown, but an informed investor knows that the stock index either will increase or decrease. Possible information spillover effects are examined within a bivariate VAR- BEKK GARCH setting, with shocks to the Swedish OMX stock index and a delta neutral OMX options strangle portfolio as approximations of directional and undirectional information. Significant conditional variance spillover effects are detected. Mainly, todays options strangle shock have an effect on tomorrows conditional index returns variance; whereas stock index shocks not appears to distress the conditional option strangle variance. This is consistent with undirectional information preceding directional information or information spillover from the option market to the stock market. Keywords: Information asymmetry, Spillover, Multivariate, VAR, GARCH JEL classification: G10; G13; G14 1 Please send correspondence to Lars Nordn, e-mail: ln@fek.su.se </li> <li> 2. Information spillover effects between stock and option markets Abstract This study analyses information spillover effects between the Swedish OMX stock index and the index option market. Two types of information are analysed in a bivariate Vectorized Autoregressive (VAR) setup with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) errors. The first type represents information where an informed investor knows whether the stock index will increase or decrease. The second type is less specific, the direction is unknown, but an informed investor knows that the stock index either will increase or decrease. Possible information spillover effects are examined within a bivariate VAR- BEKK GARCH setting, with shocks to the Swedish OMX stock index and a delta neutral OMX options strangle portfolio as approximations of directional and undirectional information. Significant conditional variance spillover effects are detected. Mainly, todays options strangle shock have an effect on tomorrows conditional index returns variance; whereas stock index shocks not appears to distress the conditional option strangle variance. This is consistent with undirectional information preceding directional information or information spillover from the option market to the stock market. Keywords: Information asymmetry, Spillover, Multivariate, VAR, GARCH JEL classification: G10; G13; G14 2 </li> <li> 3. 1. Introduction In a review article, Madhavan (2000) suggests that asymmetric information models by Copeland and Galai (1993), Glosten and Milgrom (1985), Kyle (1983), Easley and OHara (1987), Black (1993), Foster and Viswanathan (1994) have a central role in the market microstructure literature. In these models it is assumed that market makers, obliged to simultaneously quote buy and sell prices of financial assets, yielding the bid-ask spread, have an information disadvantage compared to informed investors. To protect themselves market makers have to quote bid-ask spreads large enough to compensate for losses arising from trading with these informed investors. The result is higher transaction costs for less informed investors. With the stock market in mind, two different types of information can be identified, which implies two cases of informed investors. In one case informed investors know the direction of the price of certain stocks, which uninformed investors do not know. In the other case, informed investors only know that the stock prices will change, but not whether the prices will increase or decrease. The first information type can be called directional information and the second undirectional information. The first type of informed investors is likely to trade in the stock market, whereas the second type, having undirectional information, is likely to trade in the options market. In empirical studies Cherian and Jarrow (1998) and Nandi (1999) distinguish between these two types of information. The purpose of this study is to investigate the relationship between these two types of information. In doing so, stock index and options strangle returns are modelled as a bivariate Vectorized Autoregressive (VAR) process, where the variance- covariance matrix follows a bivariate GARCH(1,1) process2 estimated with the BEKK representation suggested by Engle and Kroner (1993).3 This setup enables an investigation of lead-lag relationships, or information spillover effects, in the return and variance-covariance equations. 2 GARCH is short for Generalised Autoregressive Conditional Heteroskedasticity. See e.g. Engle (1982) and Bollerslev (1986). 3 In an early version of the paper Yoshi Baba and Dennis Kraft contributed, which led to the acronym (BEKK). 3 </li> <li> 4. This study contributes to previous research in several ways. First, the causal conjunction of information asymmetry has not been empirically quantified in a similar manner before. The BEKK model provides a framework for investigating whether directional and undirectional information are independent or if one type of information precedes the other. Intuitively, it is reasonable to assume that undirectional information leads directional information, as it is more general. Secondly, both types of information are defined as stock index and options strangle shocks. Thereby, it is possible to test informational lead-lag relationships between the stock and options market, taking into account spillover effects in the first moment (mean equations) and the second moment (variance-covariance equations). The lead-lag relationship between stock and related futures markets has been extensively researched, for example by Stoll and Whaley (1990), Chan et al. (1991) and Chan (1992), but few have studied the stock index and index options markets.4 As a final contribution, Swedish index options data are analysed. This is the first time anyone has used data from the Swedish stock and options markets in this setting. The bivariate VAR(1) full BEKK GARCH(1,1) model is adequate for stock index and options strangle returns. In the VAR equations, no significant autocorrelations are detected, indicating no information spillover effects between stock index and options strangle returns or vice versa. More importantly, significant information spillover effects between the Swedish stock market and options market is detected in the variance-covariance equations. Somewhat simplified, lagged squared stock index and options strangle shocks do affect the conditional stock index variance, whereas the conditional options strangle variance only is affected by lagged squared options strangle shocks. Likewise, the conditional covariance is significantly affected by lagged squared strangle shocks, but not by lagged squared stock index shocks. In all three conditional variance/covariance equations past vales of the conditional variance/covariance also matters. These results are consistent with the idea that undirectional information precedes directional information, or that information spills over from the option market to the stock market. 4 Ng and Pirron (1996), Koutmos and Tucker (1996) as well as Kavussanos and Nomikos (2000) explicitly study second moment spillovers between the cash and futures markets. In addition to testing first moment spillovers, Cheung and Ng (1996) realize that volatility reflects information, and that second moment (volatility) spillovers are important as well. Also, Ross (1989) argues that volatility is related to the information flow. 4 </li> <li> 5. The remainder of the study is organised as follows. Section 2 contains a description of the Swedish market for OMX-stock index options. Section 3 presents the data and the methodology of the study, whereas section 4 contains the results of the empirical analysis. The study is ended in section 5 with some concluding remarks. 2. The Swedish market for OMX index options and futures In September 1986 the Swedish exchange for options and other derivatives (OM) introduced the OMX index, a value weighted stock index based on the 30 most actively traded stocks at the Stockholm Stock Exchange (StSE). The purpose was to use the index as an underlying security for trading standardised European options and futures. Since the introduction, the trading volume has grown substantially. Presently, it is ranked among the ten largest stock index options markets worldwide.5 All derivatives at OM are traded with a fully computerised system. The trading system consists of an electronic limit order book hosted by OM. During trading hours investors submit market or limit orders to either buy or sell a certain quantity of derivative contracts. If possible, an order is matched against those already in the order book. If not, the order is stored as another limit order. The limit order book is complemented with an upstairs market. If an investor wishes to trade outside the order book he or she can phone in the order to OM. Those orders are not added to the book. Instead, OM tries to locate a counterpart and execute the order manually. Trades can also be executed outside the exchange. Such trades should be reported to OM no later than fifteen minutes prior to the opening on the subsequent trading day. All trading in derivatives at the OM is conducted by members of the exchange.6 A member is either a dealer or market maker. The trading environment constitutes a combination of an electronic matching system and market making system.7 Market makers are likely to endorse 5 The largest index options markets in the world (based on trading volume in 1993) are the S&P 100 and the S&P 500 markets in the U.S. 6 The OM is the sole owner of the London Securities and Derivative Exchange (OMLX). The two exchanges are linked to each other in real time. This means that a trader at the OMLX has access to the same limit order book as a trader at the OM. In 1995, 35 members were registered at the OM and 50 at the OMLX. 7 Compare e.g. the trading system at the CBOE, which is a continuous open-outcry auction among competitive traders; floor brokers and market makers. 5 </li> <li> 6. liquidity by quoting bid-ask spreads. Trading based only on a limit order book could exhibit problems with liquidity since the high degree of transparency may adversely affect the willingness of investors to place limit orders to the market. The trading system at StSE is based on the same kind of limit order book as at OM. However, there are no market makers. For the OMX index, European call and put options as well as futures contracts exist. On the fourth Friday each month, when the exchange is open, one series of contracts expires and another one with time to expiration equal to three months is initiated. For example, towards the end of September, the September contracts expire and are replaced with December contracts. At that time, the October (with time to expiration equal to one month) and the November contracts (with a time left to expiration equal to two months) are also listed. In addition to this maturity cycle, option and futures contracts with maturity up to two years exist. These contracts expire in January and are included in the maturity cycle when there is less than three months left to expiration. The maturity cycle applies for OMX index call and put options, as well as futures. For options a wide range of strike prices is available. Before November 28, 1997, strike prices are set at 20 index point intervals. Thereafter, starting with contracts expiring in February 1998, strikes are set wider apart at 40 index point intervals. On April 27, 1998, OM decided to split the OMX index with a factor of 4:1, and to amend the regulatory framework once again. After the split strike prices below 1,000 points are set at 10 point intervals, whereas strike prices above 1,000 points are set at 20 point intervals. When options with new expiration dates are introduced, strike prices are chosen so that they are centred at the current level of the OMX index. Further, as the stock index increases or decreases considerably, contracts with higher or lower strike prices are introduced. Thus, the range of strike prices depends on the history of the OMX index. Actual introductions of new strikes during the expiration cycle are reflected by the demand of the dealers and market makers. 6 </li> <li> 7. 3. Methodology and data The data set consists of daily closing prices for all OMX index options contracts between October 24, 1994, and June 29, 2001. The data, obtained from OM, includes closing bid-ask quotes, last transaction prices, daily high and low transaction prices, number of options contracts traded and the transacted amount in SEK as well as open interest for each contract. The bid-ask spread represent the best bid and ask quotes in the limit order book at the close of the exchange. Daily OMX index values, also obtained from OM, are constructed from daily closing transactions prices of the OMX stocks. From this data set, two daily return series are constructed, one for the OMX index and another for a delta neutral options strangle position. The stock index return on day t ( r1,t ) equals the difference between the natural logarithm of the stock index closing price on day t ( I t ) and the corresponding price on day t 1 ( I t 1 ): (1) r1,t = ln I t ln I t 1 A delta neutral options strangle position is initiated on day t 1 by buyin...</li></ul>

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