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Tangent Models As A Mathematical Framework For Dynamic Calibration


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    (Bendheim Center for Finance, ORFE, Princeton University, Princeton, NJ 08544, USA)


    (Bendheim Center for Finance, ORFE, Princeton University, Princeton, NJ 08544, USA)

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    Motivated by the desire to integrate repeated calibration procedures into a single dynamic market model, we introduce the notion of a "tangent model" in an abstract set up, and we show that this new mathematical paradigm accommodates all the recent attempts to study consistency and absence of arbitrage in market models. For the sake of illustration, we concentrate on the case when market quotes provide the prices of European call options for a specific set of strikes and maturities. While reviewing our recent results on dynamic local volatility and tangent Lévy models, we present a theory of tangent models unifying these two approaches and construct a new class of tangent Lévy models, which allows the underlying to have both continuous and pure jump components.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 01 ()
    Pages: 107-135

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:p:107-135

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    Keywords: Market models; Heath–Jarrow–Morton approach; implied volatility; local volatility; tangent Lévy models;


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    Cited by:
    1. Jan Kallsen & Paul Kr\"uhner, 2013. "On a Heath-Jarrow-Morton approach for stock options," Science & Finance (CFM) working paper archive 1305.5621, Science & Finance, Capital Fund Management, revised Aug 2013.


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