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A Minimal Share Market Model with Stochastic Volatility

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Abstract

The paper describes a continuous time share market model with a minimal number of factors. These factors are powers of Bessel processes. The asset prices are formed by ratios of the factors and have consequently leptokurtic return distributions. In this framework stochastic volatility with properties that are similar to those actually observed arises naturally. The model generates for the market index the well-known leverage effect due to negative correlation between the index and its volatility. It also incorporates possible default of an asset and thus models credit risk.

Suggested Citation

  • Eckhard Platen, 1999. "A Minimal Share Market Model with Stochastic Volatility," Research Paper Series 21, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:21
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    Citations

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    Cited by:

    1. Platen, Eckhard, 2000. "Risk premia and financial modelling without measure transformation," SFB 373 Discussion Papers 2000,92, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Robert Elliott & Eckhard Platen, 1999. "Hidden Markov Chain Filtering for Generalised Bessel Processes," Research Paper Series 23, Quantitative Finance Research Centre, University of Technology, Sydney.

    More about this item

    Keywords

    stochastic volatility; leverage effect; Bessel process; Student t distribution; minimal market model; credit risk;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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