Nonlinearities in stochastic clocks: trades and volume as subordinators of electronic markets

Abstract

This paper discusses the possibility of recovering normality of asset returns through a stochastic time change, where the appropriate economic time is determined through a simple parametric function of the cumulative number of trades and/or the cumulative volume. The existing literature argues that the re-centred cumulative number of trades could be used as the appropriate stochastic clock of the market under which asset returns are virtually Gaussian. Using tick-data for FTSE-100 futures, we show that normality is not always recovered by conditioning on the re-centred number of trades. However, it can be shown that simply extending the approach to a nonlinear function can provide a better stochastic clock of the market.