Inference from the Futures: Ranking the Noise Cancelling Accuracy of Realized Measures

Abstract

We consider the log-linear relationship between futures contracts and their underlying assets and show that in the classical Brownian semi-martingale (BSM) framework the two series must, by no-arbitrage, have the same integrated variance. We discuss the negligibility of stochastic interest rates using empirical evidence and in simulations. We then introduce the concept of noise cancellation and propose a generally applicable methodology to assess the performance of realized measures when the variable of interest is latent, overcoming the problem posed by the lack of a true value for the integrated variance. We carry out formal testing of several realized measures in the presence of noise and conduct a thorough simulation analysis to evaluate the estimators' sensitivity to different price and noise processes, sampling frequencies and stochastic components.

Cross-Sectional Noise Reduction and More Efficient Estimation of Integrated Variance

“…In this paper, however, we adopt a different perspective. Instead of transforming the price process S , we seek to mitigate the effect of noise by combining S with a different time series which enjoys the same variance as S. To this end, we will expand on Mirone (2017) and specifically focus on a futures, F , written on the series of interest, S. Suppose that in the market there are two additional assets: a risk-free asset, B, whose dynamics is given by dB t = r t dt, where r is the short rate process, and a futures written on S t with maturity T greater than t. We denote the latent efficient log futures price by F t and analogously denote by F t the observed futures price. The noise contaminating the futures is denoted by ε…”

“…In general, Equation (6) admits no closed form solution unless we impose additional assumptions on the interest rate process r. An appealing specification of r might be the CIR process (Cox et al, 1985), which together with other assumptions leads to a closed-form solution for F (see, Ramaswamy and Sundaresan, 1985). A detailed discussion about such specifications can be found in Mirone (2017) or Lunde et al (2017). In this section, we make the simple assumption that the short rate process r is deterministic.…”

“…A brief discussion on the differences between these estimators and details for their implementation can be found inMirone (2017).…”