Localizing Volatilities
Probability
2008-12-10 v1 Computational Finance
Abstract
We propose two main applications of Gy\"{o}ngy (1986)'s construction of inhomogeneous Markovian stochastic differential equations that mimick the one-dimensional marginals of continuous It\^{o} 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 results to a stochastic interest rates framework.
Keywords
Cite
@article{arxiv.math/0604316,
title = {Localizing Volatilities},
author = {Marc Atlan},
journal= {arXiv preprint arXiv:math/0604316},
year = {2008}
}