The nature of informed option trading: Evidence from the takeover market

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Chapter 2.2.1, Price discovery process in the options and stock market:

2.2.1.1, Definitions:

According to basic financial theory, an option is a redundant security whose price is derived from an 'underlying,' i.e. from a primary instrument such as a stock. Nevertheless, options can also be written on commodities, futures, and basically all assets that have an observable market price. In terms of stock options, redundancy means that every option can be replicated by a combination of the underlying stock and a risk-free bond. This holds, however, only in complete markets without transaction costs, taxes, arbitrage opportunities, and short selling constraints. The well-known and widely used option pricing model by Black and Scholes (1973) and Merton (1973) (henceforth BSM) builds upon these assumptions and derives the option price from the stock price, the strike price, the risk-free rate, the option's maturity, and the stock volatility that is expected over the life of the option. While the buyer of a call option has the right (but not the obligation) to buy a certain amount of the underlying for the strike price from the seller ('writer'), a put option entitles the holder to sell the underlying at the strike price. The contract between the buyer and the seller specifies whether the option can be exercised at any time prior to the expiration date ('American' option) or only on the day of expiration ('European' option). The BSM formula can only be applied to European calls and puts on non-dividend paying stocks. Most traded options are, however, American and need to be valued by means of other models, e.g. binomial trees.
In reality, options cannot be perfectly replicated because of transaction costs and the indivisibility of common stocks. Additionally, traders with negative private information often have no choice but to trade options in lieu of stock due to short selling constraints in the stock market. Option prices are determined by the trading activity in both stock and options markets. The large trading volumes that can be observed in the market indicate that investors take on substantial positions in derivatives. It can therefore be concluded that options are in fact non-redundant securities that are value-adding to at least some market participants.
2.2.1.2, The role of informed traders:

Since Black (1975) argued that the leverage in options could incentivize traders with private information to trade in options markets, an ever-increasing body of literature has tried to determine the role that options play in the price discovery process of stocks. In theory, new information disseminating into the marketplace should be incorporated in stock and options markets simultaneously. Yet because of market inefficiencies, this need not always be the case. Some early research in this area has revealed little evidence that options markets are particularly attractive to informed traders. For example, Vijh (1990) argues that while the implied leverage in options might attract some informed traders, this is equally true for noise traders (i.e. speculators). He measures the extent of information-related trading, using the adverse-selection component of the option's bid-ask spread (premium charged by dealers to cover losses from trades against better-informed traders) as a proxy, and finds evidence against active information trading. Stephan and Whaley (1990) compare stock price changes implied from option prices with actual stock price changes and conclude that stock markets reflect new information fifteen to twenty minutes earlier than options markets. Chan et al. (2002) focus on the net-trade volume of options and stocks and ist effect on quote revisions. The net-trade volume refers to a temporary order imbalance, or more specifically, to the difference between buyer- and seller-initiated trading volumes. While option net-trade volume does not seem to have any predictive ability, stock net-trade carries information about both stock and option quote revisions.
Nevertheless, there is substantial evidence to the contrary, namely that options markets can lead stock markets. Using their sequential trade model, Easley et al. (1998) investigate the role of option trading volume in the price discovery process. Consistent with Vijh (1990), they find no evidence that call or put option volumes predict stock prices. However, when they aggregate 'positive news" option volumes (i.e. trades entered into by traders informed of good news, e.g. buying a call or selling a put) and 'negative news" volumes (i.e. trading on bad news, e.g. buying a put or selling a call), the authors show that these aggregate volumes do in fact carry information about future stock returns, and that options markets lead stock markets by about twenty to thirty minutes (Easley et al. 1998). Pan and Poteshman (2006) apply an approach similar to Chan et al. (2002), using call and put option volumes that are initiated by buyers to open new positions. These volumes are not publicly observable. They form stock portfolios based on put-call ratios and find that the quintile portfolio with the lowest put-call ratio outperforms the one with the highest put-call ratio by over 40bps per day or 1% per week. In comparison, publicly observable signals do not seem to have predictive power. The authors conclude that the economic source of their result is the 'valuable private information in the option volume rather than an inefficiency across the stock and option market" (Pan and Poteshman 2006, p. 873). Chakravarty et al. (2004) show that informed traders trade in both stock and options markets, and estimate the option market's contribution to price discovery at about 17%. More information can be derived from options if option liquidity is high (i.e. trading volume is high, spreads are narrow) relative to stock liquidity, and if implied leverage is high. Finally, Ni et al. (2008) note that options are the preferred instruments of traders with information about future volatility (but not about the directional movement). Arguing that vega (measure for an option's exposure to volatility) is positive for both calls and puts, they construct a measure for volatility demand by treating the buy volume for calls and puts as positive demand and the sell volume as negative demand. The net volatility demand is found to predict future realized stock volatility, showing that there are informed volatility traders in the market. This effect is persistent over one week.
2.2.1.3, The predictive power of option implied volatilities:

While most of the early research on the predictive power of options uses option prices and volumes, a relatively new strand of literature is concerned with more implicit option trading proxies such as option implied volatility. The implied volatility of an option (henceforth IV) is the market's expectation of the future volatility of the underlying over the life of the option. IV is not directly observable but can be inferred from an option pricing model like BSM by using the observed market price and solving iteratively for volatility. Ceteris paribus, high IV options are more expensive than low IV options.
Cremers and Weinbaum (2010) show that the difference between implied volatilities of call and put options on the same underlying equity, with the same strike price and with the same maturity can be used to identify price pressures and predict stock returns in the cross-section. Amin et al. (2004) call this difference the implied volatility spread (henceforth IV spread). IV spreads are deviations from the put-call-parity but do not usually represent arbitrage opportunities, which is due to the fact that the put-call-parity is an inequality for American options (cf. Hull 2012) and does not account for transaction costs. Along the lines of the sequential trade model of Easley et al. (1998), Cremers and Weinbaum (2010) argue that the presence of informed investors in the options market results in option price deviations from put-call parity in the direction of the private information. It can therefore be expected that a higher call-put IV spread is indicative of positive news not yet reflected in the stock price. In fact, the authors find a positive relation between IV spread and future stock returns. A portfolio that is long in stocks with relatively expensive calls and short in stocks with relatively expensive puts earns an abnormal return of about 50bps per week. This effect is stronger when option liquidity is high and stock liquidity is low, which is consistent with the findings of Chakravarty et al. (2004). Notably, the authors control not only for the four Fama and French (1993) and Carhart (1997) factors but also for systematic return skewness, as suggested by Harvey and Siddique (2000). They justify this additional factor with the concern that stocks with high call (put) prices might have positively (negatively) skewed return distributions to begin with. Bali and Hovakimian (2009) also provide evidence for a positive relation between IV spread and future returns. In their analysis, IV spread proxies for stock price jump risk, which commands a risk premium. In addition, they theorize that the difference between the (one-month) lagged realized volatility and implied volatility proxies for volatility risk. The authors find this second spread to be negatively related to future returns. Bollerslev et al. (2009) basically come to the same conclusion. They show that the difference between (model-free) implied and realized variances positively predicts stock market returns, especially over quarterly horizons.
Another recently introduced proxy for informed option trading is implied volatility skewness (henceforth IV skew). Xing et al. (2010) define IV skew as the difference between the implied volatilities of out-of-the-money (OTM) put options and at-the-money (ATM) call options on the same underlying and with the same expiration date. OTM puts usually trade at a risk premium relative to ATM options because investors have an aversion toward negative jumps in stock prices and overestimate the probability of downward movements. This common characteristic of stock options is also known as the volatility smirk or smile. If some investors have unfavorable private information, they will buy (cheap) OTM puts. As a result, these puts become relatively expensive, which steepens the IV smirk (Xing et al. 2010). Xing et al. Find evidence that IV skew is negatively related to future stock returns, i.e. stocks exhibiting the steepest smirks underperform those with the least pronounced smirks by 21bps per week. The effect is persistent over about six months. The persistency found in the empirical literature suggests inefficiencies in the stock market that cannot instantaneously incorporate the information provided in the options market. Alternatively, it could be argued that it is not the stock market's inefficiency that drives these results but rather a misperception of the importance of the options market in the price discovery process. If the IV smirk is not regarded as a gauge of informed trading but as a measure of common investor sentiment (overly pessimistic investors buy insurance in light of increasing trading activity and volatility), stock prices will only adjust very slowly.
Doran et al. (2007) point out that option pricing models that aim to improve the model-fit over the BSM (which assumes constant volatility) need to account for the volatility smirk and incorporate a jump risk premium. For example, Bakshi et al. (1997) show that the inclusion of stock price jumps improves the performance of their stochastic volatility model, especially for the pricing of short-term options. According to Todorov (2010), the premium investors require for taking variance risk (particularly jump risk) varies over time and increases immediately after the occurrence of a price jump. This shows that extreme price movements drive the risk aversion of market participants, i.e. risk aversion is time-varying. A more detailed review of other option pricing models that include volatility and jump risk is beyond the scope of this paper. Yan (2011) provides a comprehensive survey of the most relevant works in this field. Nevertheless, the finding that both IV spread and IV skew seem to proxy for jump risk make these factors particularly intriguing with regard to event studies that explore the predictability of corporate announcements, that are expected to cause large price jumps for involved firms. The last subsection of this review will therefore focus on these announcements, especially mergers and acquisitions.