Option Prices and Stock Market Momentum

According to previous literature, we realize the long-term lead-lag relationships in the options and the underlying asset markets have less been investigated compared to the study of Price discovery in short-term. In imperfect markets, option price can be affected by the momentum of the underlying asset through a number of channels (Amin, 2003), such as investors’ expectations about future stock returns, their demand for portfolio insurance, or their attitude toward the higher moments of stock distribution. First, investors’ expectations about future stock return can depend on past stock return. Namely, it means that price movements in the underlying asset market cause price pressures in the options market at a later market, which suggests that a rise in the asset price triggers trading in the options market.

This kind of trading behavior is known as momentum trading and is described in the literature extensively by several authors. Delong, Shleifer, Summers, and Waldmann (1990) introduce positive feedback (momentum) traders, who buy when prices rise and sell when prices fall and who may have a variety of incentives for this behavior. These incentives include trend chasing, inability to meet margin call, or portfolio insurance. Inform traders anticipating the behavior of momentum investors alter their trading behavior to profit from the follower’s expected reaction. Therefore, informed traders buy more than what the fundamental value would suggest which reinforces the trading by positive feedback traders and drives the price

above its fundamental value. Lo and Mackinlay (1988) show that the cross-sectional interaction of security returns over time is an important aspect of stock price dynamics. As an example, we document the fact that stock returns are often positively cross-autocorrelation, which reconciles the negative serial dependence in individual security returns with the positive auto correlation in market indexes. Jegadeesh and Timan (1993) constructed trading strategies which buy past winners and sell past losers realize significant abnormal returns over the 1965 to 1989. For example, the strategy they examine in most detail, which select stock based on their past 6-month returns and holds them for 6 months, realizes a compounded excess return of 12.01% per year on average. The returns of the zero-cost winners minus losers portfolio were examined in each of the 36 months following the portfolio formation date. With the exception of the first month, of the first month, this portfolio realizes positive returns in each of the 12 months after the formation date. However, the longer-term performances of these past winners and losers reveal that half of their excess returns in the year following the portfolio formation date dissipate within the following 2 years.

Chan, K. C.’s (1998) contrarian stock selection strategy consists of buying stocks that have been losers and selling short stocks that have been winners. Preached by market practitioners for years, it is still in vogue on Wall Street and La Salle Street. The strategy is formulated on the premise that the stock market overreacts to news, so winners tend to be overvalued and losers undervalued; an investor who exploits this inefficiency gains when stock prices revert to fundamental values. Many investment strategies, such as those based on the price/earnings ratio, or the book/market ratio, can be regarded as variants of this strategy.

Conrad, Kaul, and Nimalendran (1998) also constructed trading strategies buying past winners and selling past losers to realize that momentum trading strategy was profited for short-term period (one month) and long-term period (3-years to 5- years) and reversal trading strategy was profited for medium term (3-month to 1-year).

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Hong and Stein (1999) recognize momentum traders as those who condition their trades only on past price changed. This simple trading rule, along with a gradual release of information to news watchers allows for both short-term under-reaction and long-term over-reaction. Hence, if past returns are strongly positive, positive autocorrelation suggests that future stock returns will also be greater than average. Investors can exploit this expectation by buying call options on the market index, thereby creating an upward pressure on call prices. Similarly, if past returns are negative, then future stock returns are projected to be below average. Investors can exploit this expectation by buying put options on the market index, creating an upward pressure on put prices. This is cross-market momentum that the option prices depend on the past manifestation of spot market. Additionally, many researcher consider the momentum trading is common phenomenon for all kinds of financial investment.

Hence, if past returns are strongly positive, positive autocorrelation suggests that future stock returns will also be greater than average. Investors can exploit this expectation by buying call options on the market index, thereby creating an upward pressure on call prices. Similarly, if past returns are negative, then future stock returns are projected to be below average.

Investors can exploit this expectation by buying put options on the market index, creating an upward pressure on put prices. This phenomenon is cross momentum behavior which past performance transfer to option market.

Second, portfolio insurance consideration suggests that the degree to which market participants want exposure to stock prices can depend on recent stock market movement, which then affects the supply and demand for calls and puts. An easy way of changing the exposure to the stock market is by buying call and put options on a stock market index. If, after market prices have risen, an increased number of market participants demand greater exposure to equities, they can purchase call options on a market index, thereby putting upward pressure on call prices. In this case, all prices rise to increase the supply of call writers.

If, after market prices have fallen, an increased number of market participants demand smaller exposure to equities, they can purchase put options on a market index, thereby putting upward pressure on put prices. In this case, put prices rise to increase the supply of put writers.

Third, past stock returns can change investors’ expectations about the higher moments of stock prices. If investors care about higher moments, then their demand for call and put options can change as their expectations about higher moments change, again creating pressures in call and put prices. For example, previous researches in the stock market have found that investors prefer skewness in stock returns. Once again, changes in market momentum can affect the supply and demand for option by changing investor’ skewness in stock returns.

For stock and option market, Tavakkol (2000) conceived that all of these study probe the short-term relationship (intra-day and next day), as they focus on quick information transfers across markets. Even though the autocorrelation and cross-correlation studies in equity markets cover longer periods of time, the long-term lead-lag relationships in options and the underlying asset markets have not been investigated. They use Black’s (1976) model to calculate implied volatilities and the volatility spread at the end of period t is calculated as the difference between the simple average implied volatility of calls and the corresponding average for puts. The one- to 12-month S&P futures returns are used as momentum variable for spot market. They examined the relationship between option market and spot market by OLS estimates of the regressions of volatility spread on lagged spot market returns and indicated prior one-month and three-month returns on S&P future contracts have explanatory power over volatility spreads observed at the end of the period. This means that buying in the asset market over a one- to three-month period is associated with upward pressure on calls and downward pressure on puts. This positive pressure, triggered by long call and short put trades, increases the implied volatility for calls and lowers the implied volatility for puts, thus

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reducing the volatility spread at the end of the period, and vice versa. Furthermore, the stabilizing effect of feedback trading is also tested in their study. i.e. , whether the activities in the options market are strong enough to cause a reversal in the underlying market. This result supports the reversion hypothesis and the empirical evidence reported for equity market by Jegadeesh an Titman (1993).

Amin, Coval and Seyhun (2004) adopted the Standard and Poor’s 100 Index (also called OEC options) and the market returns are computed using the value-weighted index of NYSE, AMEX, and NASDAQ stocks to investigate the relationship between option market and stock market. At the beginning, they constructed the Boundary Condition Tests Based on Put-Call Parity for American Options. An increase in past stock returns causes the probability of boundary violation to increase and the magnitude of the arbitrage violation is also added. This observation are acknowledged that stock momentum have a significant impact on option market. Next, They formulated a parametric approach instead of the nonparametric boundary condition violations. The parametric measure of the price pressures in option markets is the implied volatility of call and put prices. Implied volatility is computed using the escrowed dividend modification of the binomial model employed in Harvey and Whaley (1992).

Similarly, the relationship between option market and stock market are examined. Their finding is like Tavakkol’s result that past returns is the pressure for option prices. In addition, They suggested that standard option pricing model and past returns are independent is not correct and there is no perfect arbitrage activities to reach the equilibrium of market price.

3. Data and Methodology