A parsimonious continuous time model of equity index returns (inferred from high frequency data)

In this paper we propose a continuous time model capable of describing the dynamics of futures equity index returns at different time frequencies. Unlike several related works in the literature, we avoid specifying a model a priori and we attempt, instead, to infer it from the analysis of a data set of 5-minute returns on the S&P500 futures contract. We start with a very general specification. First we model the seasonal pattern in intraday volatility. Once we correct for this component, we aggregate intraday data into a daily volatility measure to reduce the amount of noise and its distorting impact on the results. We then employ this measure to infer the structure of the stochastic volatility model and of the leverage component, as well as to obtain insights on the shape of the distribution of conditional returns. Our model is then refined at a high frequency level by means of a simple nonlinear filtering technique, which provides an intraday update of volatility and return densityestimates on the basis of observed 5-minute returns. The results from a Monte Carlo experiment indicate that a sample of returns simulated according to our model successfully replicates the main features observed in market returns.