• Mathematics, Economics
  • Published 2004

Localizing Volatilities

@inproceedings{Atlan2004LocalizingV,
  title={Localizing Volatilities},
  author={Marc Atlan},
  year={2004}
}
We propose two main applications of Gyöngy (1986)'s construction of inhomogeneous Markovian stochastic differential equations that mimick the one-dimensional marginals of continuous Itô processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)'s result. We then present Bessel-based stochastic volatility models in which this relation is used to compute analytical formulas for the local volatility. Secondly, we use these mimicking techniques to extend the well-known local volatility… CONTINUE READING

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