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
