On Latency and Volatility

Abstract

How does latency affect the dynamics of asset prices in modern markets? In this paper, we present a simple model of latency. In our model, latency is a delay between the observed asset price and its true, but latent fundamental price. Because of latency, the observed asset price shadows the true price at some deformed distance away. In other words, latency leads to the deformation in the clock of an asset's evolution. Deformation in the clock links latency to fluctuations in volatility; so, latency should be in some way related to the volatility of volatility. A standard way to characterize the volatility of volatility, however, hinges upon first estimating volatility at an intermediate fixed time scale, and then looking at the fluctuations of volatility. This is going to miss the effect of latency. Instead, we define a volatility of instantaneous volatility (VIV), which pushes the notion of the volatility of volatility down to a microscopic level and enables us to link volatility to latency. We demonstrate the link between the VIV and latency first for a fixed latency and then suggest how to generalize it to stochastic, evolving latency. While the intuition that latency ends up in the volatility of volatility is simple, the math quickly gets out of hand as we need to keep track of many moving parts inside deformed clocks. We go through all this math because we believe that with the continuing automation of the trading process, latency itself has become a market factor which should be explicitly modeled and then - when the models become robust like those for volatility - traded. Traders who wish to hedge their exposure to or speculate on marketwide latency can take positions in something akin to the VIX; we call the LIX - the Latency Index. This could help price the latency risk and allocate it around.