Change of drift in one-dimensional diffusions
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 tha...
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| Veröffentlicht in: | Finance and stochastics 2021-04, Vol.25 (2), p.359-381 |
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| container_title | Finance and stochastics |
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| creator | Desmettre, Sascha Leobacher, Gunther Rogers, L. C. G. |
| description | 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. |
| doi_str_mv | 10.1007/s00780-021-00451-w |
| format | Article |
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| source | Business Source Complete; SpringerLink Journals - AutoHoldings |
| subjects | Arbitrage Diffusion Dimensional changes Drift Economic Theory/Quantitative Economics/Mathematical Methods Economics Finance Growth rate Insurance Management Martingales Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Quantitative Finance Statistics for Business Volatility |
| title | Change of drift in one-dimensional diffusions |
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