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

Marc Decamps, Ann De Schepper () and Marc Goovaerts

Working Papers from University of Antwerp, Faculty of Business and Economics

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.

Pages: 29 pages
New Economics Papers: this item is included in nep-fin
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Persistent link: https://EconPapers.repec.org/RePEc:ant:wpaper:2003027

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