Change of drift in one-dimensional diffusions

2019/10/25 by Desmettre, Sascha, Leobacher, Gunther, Rogers, L. C. G. · 3 citations
#FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · doi:10.48550/arxiv.1910.11904

Abstract

It is generally understood that a given one-dimensional diffusion may be transformed by Cameron-Martin-Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this we have to know that the change-of-measure local martingale that we write down is a true martingale; we provide a complete characterization of when this happens. This is then used to discuss absence of arbitrage in a generalized Heston model including the case where the Feller condition for the volatility process is violated.

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