WHAT (REALLY) DRIVES PUT-CALL PARITY VIOLATIONS IN S&P 500 INDEX OPTIONS?

Abstract

The purpose of this study is two-fold. First, I analyze the relative contribution of a number of different factors to Put-Call Parity (PCP henceforth) violations in a set of (European-like) S&P 500 index options (SPX henceforth), for the period between 2004 and 2011. Second, I study whether PCP violations represent cases of mispricing in SPX and whether a profitable strategy can be constructed based on the signals provided by such violations. PCP is derived from the Black-Scholes-Merton option pricing model, which is based on a number of simplifying assumptions. In particular, trading costs, margin requirements, heterogeneity in beliefs, and investor sentiment, are some of the realworld factors not considered in the Black-Scholes-Merton model. The existence of such factors in the real-world can therefore lead to the PCP violations. I show that investor sentiment factors are, as a group, among all the factors considered in this study, the factors that have higher statistical power in explaining PCP violations. Even though PCP violations are easily observable, taking advantage of such violations can be a hard task, which may be the reason why PCP violations are persistent over time. PCP is a no-arbitrage relation which may help investors detect mispricing in European-type options’ prices. If such mispricing really is represented in a PCP violation, then investors might be able to profit from them. I identify PCP violations in European-type options, like the SPX, by looking at the difference between the implied volatility of call and put options with the same strike price and the same time ii to expiration. I investigate the profitability associated with PCP violations by creating an options trading strategy that uses volatility spreads as trading signals. I show the existence of the weekend effect in SPX returns, consistent with what has been shown in existing literature for options on individual stocks. However, the volatility spreads in SPX do not provide me any conclusive trading signal on a daily frequency. However, consistent with the result that volatility spreads are persistent over time, I show that investors might be able to profit from mispricing of options as given by PCP violations, by considering holding periods of at least 20 trading days. I show that the returns of this strategy can be quite substantial, given the convexity in the payoff structure of these instruments. However, such results have to be taken with caution, as trading on such instruments can be incredibly risky