Bivariate support of forward libor and swap rates

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Jamshidian, Farshid (2008) Bivariate support of forward libor and swap rates. Mathematical Finance, 18 (3). pp. 427-443. ISSN 0960-1627

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Abstract:Based on a certain notion of "prolific process," we find an explicit expression for the bivariate (topological) support of the solution to a particular class of 2 × 2 stochastic differential equations that includes those of the three-period "lognormal" Libor and swap market models. This yields that in the lognormal swap market model (SMM), the support of the 1 × 1 forward Libor L*t equals [l*t, ∞) for some semi-explicit −1 ≤l*t≤ 0 , sharpening a result of Davis and Mataix-Pastor (2007) that forward Libor rates (eventually) become negative with positive probability in the lognormal SMM. We classify the instances l*t < 0 , and explicitly calculate the threshold time at or before which L*t remains positive a.s.
Item Type:Article
Copyright:© 2008 Wiley InterScience
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/72364
Official URL:http://dx.doi.org/10.1111/j.1467-9965.2008.00340.x
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