Yet more on a stochastic economic model: Part 3C: stochastic bridging for share yields and dividends and interest rates

Abstract

AbstractThis is the third and last subpart of a long paper in which we consider stochastic interpolation for the Wilkie asset model, considering both Brownian bridges and Ornstein–Uhlenbeck (OU) bridges. In Part 3A, we developed certain properties for both these types of stochastic bridge, and in Part 3B we investigated retail prices and wages. In this paper, we investigate the remainder of many of our data series, relating to shares and interest rates. We conclude that, regardless of the form of the annual model, the monthly data within each year can be modelled by Brownian bridges, usually on the logarithm of the principal variable. But in no case is a simple Brownian bridge enough, and all series have their own peculiarities. Overall, however, our modelling produces simulations that are realistic in comparison with the known data. Many of our findings would apply to any similar model used for simulation over time. Our results have considerable importance for financial economics. We reconcile the conflict between the long-term mean-reverting modelling of Schiller and the short-term random walk modelling of Fama. This conclusion therefore has very wide significance.