Path integrals as a tool for pricing interest rate contingent claims: the case of reflecting and absorbing boundaries
AbstractCommon interest rate models are faced with the problem of volatilities vanishing for spot rates in the vicinity of zero. A possible answer to this difficulty can be given by the introduction of a reflecting boundary at zero, at the same time guaranteeing the spot rate to be non-negative, which is needed in order to avoid the possibility of arbitrage. In the present paper, we obtain closed form expressions for transition probabilities and for prices of general interest rate contingent claims by means of path integrals, when the spot rate process is modelled by means of a general diffusion with a reflecting or absorbing boundary. We also show how to derive accurate closed form approximations in case the path integrals are not analytically computable.
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Bibliographic InfoPaper provided by University of Antwerp, Faculty of Applied Economics in its series Working Papers with number 2003027.
Length: 29 pages
Date of creation: Dec 2003
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