Innovations in Derivatives Markets by Kathrin Glau Zorana Grbac Matthias Scherer & Rudi Zagst
Author:Kathrin Glau, Zorana Grbac, Matthias Scherer & Rudi Zagst
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham
(8)
Recall that, for simplicity of exposition, we consider a single Libor for a single tenor and so also a single fictitious bond. In general, one has one Libor and one fictitious bond for each tenor, i.e. and . Note that we shall model the bond prices , for all t and T with , even though only the prices , for all T, are needed in relation (8). Moreover, keeping in mind that the bonds are fictitious, they do not have to satisfy the boundary condition , but we still assume this condition in order to simplify the modeling.
To derive a dynamic model for , we may now derive a dynamic model for , where we have to keep in mind that the latter is not a traded quantity. Inspired by a credit-risk analogy, but also by a common practice of deriving multi-curve quantities by adding a spread over the corresponding single-curve (risk-free) quantities, which in this case is the short rate , let us define then the Libor (risky) bond prices as
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