A Parsimonious Continuous Time Model for Equity Returns
44 Pages Posted: 26 Apr 2003
Date Written: January 15, 2003
In this paper we propose a parsimonious continuous time model capable of describing and replicating the dynamics of equity returns. Unlike several related works in the literature, we avoid specifying a model a priori and we try, instead, to infer our model from the analysis of a data set of 5-minute returns on the S&P500 future contract. We start with a very general model structure and we perform a careful step by step analysis of the data, recording the relevant features that need to be modelled, whose peculiar characteristics will actually drive the choice amongst different possible specification errors by testing all the assumptions we make. Throughout the entire paper we try to keep the modelling assumptions to a minimum, while retaining an adequate level of structure. The findings from our analysis suggest a model where: 1. The seasonal intraday volatility component is deterministic and constant through time. 2. The stochastic volatility component is independent from the seasonal one and is well described by a two-factor mean reverting process with volatility forecasts updated every 5 minutes according to a non-linear filtering technique. 3. The conditional return distribution turns out to be surprisingly close to a gaussian and remarkably constant across the different intraday intervals. The results from a Monte Carlo experiment indicate that a sample of returns simulated according to our model exhibits the main features observed in market returns. Extensions aimed at modelling the leverage effect aimed at including a jump component in the returns are currently being investigated.
JEL Classification: C11, C51, C52, C53, G12
Suggested Citation: Suggested Citation