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Stochastic Volatility Models

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Fundamentals and Advanced Techniques in Derivatives Hedging

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Abstract

Stochastic volatility models are used when the option price is very sensitive to volatility (smile) moves, and when they cannot be explained by the evolution of the underlying asset itself, see e.g. [34]. This is typically the case for exotic options.

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Notes

  1. 1.

    One can also use asymptotic results, see e.g. [7].

  2. 2.

    In Exercise 7.5, the function \(\hat{\sigma }\) is fixed, the only inputs/parameters are the call prices (C i) i ≤ I .

  3. 3.

    One can in fact construct a model of price process S such that equality holds.

  4. 4.

    This is the implied volatility associated to our LSV model.

  5. 5.

    See Exercise 2.4.

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Authors and Affiliations

  1. Université Paris Dauphine, Paris, France

    Bruno Bouchard

  2. Université Paris Diderot, Paris, France

    Jean-François Chassagneux

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  1. Bruno Bouchard
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  2. Jean-François Chassagneux
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Bouchard, B., Chassagneux, JF. (2016). Stochastic Volatility Models. In: Fundamentals and Advanced Techniques in Derivatives Hedging. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-38990-5_8

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