Change of drift in one-dimensional diffusions

Sascha Desmettre; Gunther Leobacher; L. C. G. Rogers

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arXiv · 1910.11904

Change of drift in one-dimensional diffusions

Sascha Desmettre·Gunther Leobacher·L. C. G. Rogers

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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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Sascha Desmettre, Gunther Leobacher, L. C. G. Rogers. 2019-10-25. Change of drift in one-dimensional diffusions. https://arxiv.org/abs/1910.11904

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