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Sensitivity analysis in a market with memory

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  • David R. Banos
  • Giulia Di Nunno
  • Frank Proske
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    Abstract

    A general market model with memory is considered. The formulation is given in terms of stochastic functional di?erential equations, which allow for ?exibility in the modeling of market memory and delays. We focus on the sensitivity analysis of the dependence of option prices on the memory. This implies a generalization of the concept of delta. Our techniques use Malliavin calculus and Fr\'echet derivation. When it comes to option prices, we consider both the risk-neutral and the benchmark approaches and we compute the delta in both cases. Some examples are provided.

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    File URL: http://arxiv.org/pdf/1312.5116
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1312.5116.

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    Date of creation: Dec 2013
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    Handle: RePEc:arx:papers:1312.5116

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    Web page: http://arxiv.org/

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    1. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Uwe K├╝chler & Eckhard Platen, 2007. "Time Delay and Noise Explaining Cyclical Fluctuations in Prices of Commodities," Research Paper Series 195, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Eckhard Platen, 2005. "On the Role of the Growth Optimal Portfolio in Finance," Research Paper Series 144, Quantitative Finance Research Centre, University of Technology, Sydney.
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