Lévy term structure models: no-arbitrage and completeness. (English) Zbl 1065.60086
The term structure models driven by Lévy processes are considered from the point of view of their no-arbitrage property and completeness. The authors take a driving process that is not necessarily a Lévy process but which has independent increments and absolutely continuous characteristics. Its natural name is ‘non-homogeneous Lévy process’. Classes of equivalent martingale and local martingale measures for various filtrations are characterized. A somewhat surprising result is that in the case of one-dimensional driving process a Black-Scholes type situation arises: there is a unique equivalent martingale measure.
Reviewer: Yuliya S. Mishura (Kyïv)
MSC:
60H30 | Applications of stochastic analysis (to PDEs, etc.) |
91G30 | Interest rates, asset pricing, etc. (stochastic models) |
60G51 | Processes with independent increments; Lévy processes |