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

Published online by Cambridge University Press:  24 November 2016

A. D. Wilkie*
Affiliation:
InQA Limited, Dennington, Ridgeway, Horsell, Woking GU21 4QR, UK
Şule Şahin
Affiliation:
Department of Actuarial Sciences, Hacettepe University, 06800 Ankara, Turkey
*
*Correspondence to: A. D. Wilkie, InQA Limited, Dennington, Ridgeway, Horsell, Woking GU21 4QR, UK. Tel. +441483 725984 or 01483 725984; E-mail: david.wilkie@inqa.com

Abstract

This 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.

Type
Papers
Copyright
© Institute and Faculty of Actuaries 2016 

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References

Wilkie, A.D. (1986) A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341381.CrossRefGoogle Scholar
Wilkie, A.D. (1995) More on a stochastic asset model for actuarial use. British Actuarial Journal, 1, 777964.CrossRefGoogle Scholar
Wilkie, A.D. & Şahin, Ş. (2016). Yet more on a stochastic economic model: Part 2: initial conditions, select periods and neutralising parameters. Annals of Actuarial Science, 10, 151.CrossRefGoogle Scholar
Wilkie, A.D., Şahin, Ş., Cairns, A.J.G. & Kleinow, T. (2011). Yet more on a stochastic economic model: Part 1: updating and refitting, 1995 to 2009. Annals of Actuarial Science, 5, 5399.CrossRefGoogle Scholar
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