An Interest Rate Model with Upper and Lower Bounds View Full Text


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Article Info

DATE

2002-09

AUTHORS

Freddy Delbaen, Hiroshi Shirakawa

ABSTRACT

We propose a new interest rate dynamicsmodel where the interest rates fluctuate in a bounded region. The model ischaracterised by five parameters which are sufficiently flexible to reflect theprediction of the future interest rates distribution. The interest rate convergesin law to a Beta distribution and has transition probabilities which arerepresented by a series of Jacobi polynomials. We derive the moment evaluationformula of the interest rate. We also derive the arbitrage free pure discountbond price formula by a weighted series of Jacobi polynomials. Furthermore wegive simple lower and upper bounds for the arbitrage free discount bond pricewhich are tight for the narrow interest rates region case. Finally we show thatthe numerical evaluation procedure converges to the exact value in the limitand evaluate the accuracy of the approximation formulas for the discount bondprices. More... »

PAGES

191-209

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1024125430287

DOI

http://dx.doi.org/10.1023/a:1024125430287

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1010653400


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