2006/04/13 by Marc Atlan, Atlan, Marc
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Market Dynamics and Volatility #Probability (math.PR) #math.PR #q-fin.CP
paper · pdf · doi:10.48550/arxiv.math/0604316
arxiv created 2006/04/13 · openalex publication_date 2006/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 results to a stochastic interest rates framework.