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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.

Suggested Citation

  • DECAMPS, Marc & DE SCHEPPER, Ann & GOOVAERTS, Marc, "undated". "Path integrals as a tool for pricing interest rate contingent claims: The case of reflecting and absorbing boundaries," Working Papers 2003027, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2003027
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    References listed on IDEAS

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