Change of drift in one-dimensional diffusions
Mathematical Finance
2020-12-08 v4
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.
Cite
@article{arxiv.1910.11904,
title = {Change of drift in one-dimensional diffusions},
author = {Sascha Desmettre and Gunther Leobacher and L. C. G. Rogers},
journal= {arXiv preprint arXiv:1910.11904},
year = {2020}
}