On Modelling Long Term Stock Returns with Ergodic Diffusion Processes: Arbitrage and Arbitrage-Free Specifications

29 Pages Posted: 19 Nov 2008

See all articles by Bernard Wong

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: November 18, 2008

Abstract

We investigate the arbitrage-free property of stock price models where the local martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for insurer asset-liability management as they allow the modelling of long term stock returns with heavy tailed ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market. Unfortunately the standard specification of these models in the literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities, and consequently construct a modification that is arbitrage free.

JEL Classification: C16, G13

Suggested Citation

Wong, Bernard, On Modelling Long Term Stock Returns with Ergodic Diffusion Processes: Arbitrage and Arbitrage-Free Specifications (November 18, 2008). UNSW Australian School of Business Research Paper No. 2008ACTL17, Available at SSRN: https://ssrn.com/abstract=1303845 or http://dx.doi.org/10.2139/ssrn.1303845

Bernard Wong (Contact Author)

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

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