On market efficiency and volatility estimation

We propose a non-parametric procedure for estimating the realized spot volatility of a price process described by an Itô semimartingale with Lévy jumps. The procedure integrates threshold jump elimination technique of Mancini (2009) with a frame (Gabor) expansion of the realized trajectory of spot volatility. We show that the procedure converges in probability in L²([0; T]) for a wide class of spot volatility processes, including those with discontinuous paths. Our analysis assumes the time interval between price observations tends to zero; as a result, the intended application is for the analysis of high frequency financial data. We investigate practical tests of market efficiency that are not subject to the joint-hypothesis problem inherent in tests that require the specification of an equilibrium model of asset prices. The methodology we propose simplify the testing procedure considerably by reframing the market efficiency question into one about the existence of a local martingale measure. As a consequence, the need to directly verify the no dominance condition is completely avoided. We also investigate market efficiency in the large financial market setting with the introduction of notions of asymptotic no dominance and market efficiency that remain consistent with the small market theory. We obtain a change of numeraire characterization of asymptotic market efficiency and suggest empirical tests of inefficiency in large financial markets. We argue empirically that the U.S. treasury futures market is informational inefficient. We show that an intraday strategy based on the assumption of cointegrated treasury futures prices earns statistically significant excess return over the equally weighted portfolio of treasury futures. We also provide empirical backing for the claim that the same strategy, financed by taking a short position in the 2-Year treasury futures contract, gives rise to a statistical arbitrage.