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BIVARIATE SUPPORT OF FORWARD LIBOR AND SWAP RATES
Author(s) -
Jamshidian Farshid
Publication year - 2008
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2008.00340.x
Subject(s) - libor , bivariate analysis , interest rate swap , libor market model , log normal distribution , swap (finance) , econometrics , mathematics , forward rate , economics , interest rate , mathematical economics , statistics , finance , volatility (finance)
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.