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Perfect Hedging of Index Derivatives Under a Locally Arbitrage Free Minimal Market Model

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Abstract

The paper presents a financial market model that generates stochastic volatility using a minimal set of factors. These factors, formed from transformations of square root processes, model the dynamics of different denominations of a benchmark portfolio. Benchmarked prices are assumed to be local martingales. Numerical results for the pricing and hedging of basic derivatives on indices are described. This includes cases where the standard risk neutral pricing methodology fails. However, payoffs can be perfectly hedged using self-financing strategies and a form of arbitrage still exists. This is illustrated by hedge simulations. The term structure of implied volatilities is documented.

Suggested Citation

  • David Heath & Eckhard Platen, 2001. "Perfect Hedging of Index Derivatives Under a Locally Arbitrage Free Minimal Market Model," Research Paper Series 61, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:61
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp61.pdf
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    References listed on IDEAS

    as
    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. Platen, Eckhard, 2001. "A benchmark model for financial markets," SFB 373 Discussion Papers 2001,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    More about this item

    Keywords

    derivative pricing; arbitrage; minimal market model;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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