Change of drift in one-dimensional diffusions

Sascha Desmettre (), Gunther Leobacher and L. C. G. Rogers
Additional contact information
Sascha Desmettre: Johannes Kepler University Linz
Gunther Leobacher: University of Graz
L. C. G. Rogers: University of Cambridge

Finance and Stochastics, 2021, vol. 25, issue 2, No 6, 359-381

Abstract: Abstract It is generally understood that a given one-dimensional diffusion may be transformed by a 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 characterisation of when this happens. This enables us to discuss the absence of arbitrage in a generalised Heston model including the case where the Feller condition for the volatility process is violated.

Keywords: One-dimensional diffusions; Change of measure; Heston model; Feller condition; Free lunch with vanishing risk; 60J60; 91B70 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00780-021-00451-w

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