COMPARING PRICE MOVEMENTS OF OPTIONS AND THE UNDERLYING INDEX

In theory, a call option and its underlying index should move in the same direction, while a put option and its underlying index should move in opposite directions. This property is referred to as the Empirical Monotonicity Property (EMP) when applied to time series of prices. In this paper, we use daily call and put options? data to conduct empirical tests of the EMP, including three violation types. Further, we investigate the effect of grouping the option prices by their Black-Scholes implied volatility and by moneyness, and also the effect of using different quotes (bid, offer, and bid-offer midpoint). In addition to EMP, which depends on the signs of the price changes, we also test another theoretical constraint concerning the magnitude of these changes. This is followed by a discussion of the possible causes for violations of the EMP. We use regression analysis to test whether volatility changes may be one of these causes. Lastly, we summarize the implications of our study to hedging strategies.