An Information-Based Model of Market Volatility

Abstract

A model for volatility, based on the relation between volatility and information flows, leads to the specification of a stochastic process for volatility. This allows one to compute potentially useful properties, such as the probability that volatility will change from one level to another within a specific time period. The model relies on three characteristics of information. (1) Information arrives in discrete packets, and the probability of its arrival is a function of time. (2) Different pieces of information have different degrees of impact on the market, hence on the market's volatility. (3) It takes time for the market to digest information; the greater the impact of the information, the longer its effect on volatility will last. Comparison of actual daily volatility for the Treasury bond yield with the volatility given by the information-based model shows clear similarities between the frequencies of variability, the ranges of volatility, the speeds with which spikes dampen and the longer-term waviness of the processes. The model also did well in explaining equity market volatility following the 1987 crash. The model suggests that volatility is mean-reverting. The tendency is for above-average volatility to decline and for below-average volatility to increase. The nature of the information flows underlying the model suggests that volatility can be expected to be reasonably stable over long time periods; the mean level of volatility may not change dramatically, even over five or 10 years.