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Path integrals as a tool for pricing interest rate contingent claims: The case of reflecting and absorbing boundaries

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  • DECAMPS, Marc
  • DE SCHEPPER, Ann
  • GOOVAERTS, Marc

Abstract

Common 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 probalities 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 Info

Paper provided by University of Antwerp, Faculty of Applied Economics in its series Working Papers with number 2003027.

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Length: 29 pages
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Handle: RePEc:ant:wpaper:2003027

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Web page: https://www.uantwerp.be/en/faculties/applied-economic-sciences/
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