On Modelling Long Term Stock Returns with Ergodic Diffusion Processes: Arbitrage and Arbitrage‐Free Specifications | Zendy

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

Author(s) -

Bernard Wong

Publication year - 2009

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2009/215817

Subject(s) - arbitrage , ergodic theory , index arbitrage , arbitrage pricing theory , martingale (probability theory) , econometrics , risk arbitrage , mathematics , trading strategy , economics , mathematical economics , capital asset pricing model , financial economics , mathematical analysis

We investigate the arbitrage-free property of stock price models where the localmartingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in 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

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