Standard option pricing models, such as the Black-Scholes model and binomial model, assume perfect capital markets, a martingale diffusion process for underlying asset returns and replicability of option payoffs using the underlying asset and the risk-free asset. Under these assumptions, options are priced by disallowing arbitrage opportunities. Hence, standard models predict that only six factors enter into the option pricing formulas: the price of the underlying asset, exercise price, time to maturity, risk-free interest rate, volatility and dividends on the underlying asset. Other factors which may affect the price of the underlying asset, such as expected future stock returns and investors’ preferences about the higher moments of the underlying asset return distributions, are not priced.
However, when the perfect market assumption is relaxed, it becomes difficult to replicate option payoffs. Consequently, option prices can deviate from the prices of the replicating portfolios, and to some extent, become non-redundant securities [Figlewski (1989), Figlewski and Webb (1993) and Grossman (1995)]. Prices of the non-redundant securities are then determined both by the supply and demand for these securities as well as limited arbitrage considerations in imperfect markets. This approach opens up the possibility that additional factors could enter into option pricing. Specifically, stock market momentum can change investors’ risk aversion and their perceptions about the mean, volatility, or the higher moments of the underlying stock market return distribution and thereby affect the supply and demand for options. In this paper, we test the predictions of the standard option pricing models that there should be no relation between the option prices and the stock market momentum.
While there is a large literature on the importance of momentum in pricing of stocks, the relation between momentum and option pricing has not been examined. In imperfect markets, option prices can be affected by the momentum of the underlying asset through a number of channels, such as investors’ expectations about future stock returns, their demand for portfolio insurance, or their attitude towards the higher moments of stock return distributions. First, investors’ expectations about future stock returns can depend on past stock returns. Lo and MacKinlay (1988) show that the value-weighted market index shows strong positive auto-correlation of returns up to four-month horizons. Hence, if past returns are strongly positive, positive auto-correlation 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 will be 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. Second, portfolio insurance consideration suggests that the degree to which market participants want exposure to stock prices can depend on recent stock market movements, 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, call prices will 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 will rise to increase the supply of put writers. Finally, 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 instance, previous research in the stock market has found that investors prefer skewness in stock returns. Once again, changes in market momentum can affect the supply and demand for options by changing investors’ skewness expectations.
Our study is related to Stein (1989) and Lo and Wang (1995). Stein (1989) shows that long-term calls and puts overreact to volatility shocks, relative to short-term options. Our study differs from Stein (1989) in that we examine if investors bid up prices of call options after market advances and bid up prices of put options after market declines. Lo and Wang (1995) consider the implications of the predictability of stock returns on the estimates of historical volatility and on option pricing. Our objective differs from that of Lo and Wang in that we do not constrain the pricing effects to occur through the overall volatility estimates. Instead, we look for relative divergence between call and put option prices as a function of past stock returns.
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