Non-parametric analysis of equity arbitrage

- The significance of log bases is evident via rejecting the unbiasedness model hypotheses.
- The arbitrage price, return, volatility and correlation series are explained by illiquidity.
- The Options/Stock trading volume ratio is significantly explained by arbitrage.
- The duration of arbitrage opportunities is 1.2 minutes (72 seconds).
- Risk premium, jumps, arbitrage, realized skewness and option trading volume explain arbitrage.

Arbitrage is non-parametrically examined and empirically analyzed in US equity markets. Firstly, analyzed are the properties of arbitrage; and secondly, the factors explaining arbitrage are tested. Empirical analysis concerns a decade of intraday data of five US equity indices and is also implemented in both daily and intraday frequencies. The cost-of-carry model (log base) significantly quantifies arbitrage in the US equity markets. The properties of the log-base arbitrage are similar to the ones expected and to those of the implied arbitrage as well. The significance of the cost-of-carry model (log-bases in the levels of price, return and volatility series) is also proved by rejecting the unbiasedness hypotheses of the model. The arbitrage price, return, volatility and correlation series are significantly explained by illiquidity. The Options/Stock trading volume ratio is significantly explained by arbitrage. The duration of arbitrage opportunities is 1.2 min (72 s), indicating that the market eliminates profitable deviations rather quickly. Volatility risk premium, jump risk, lagged arbitrage returns, realized skewness implied ratio, and option trading volume significantly explain arbitrage.