Interest-Rate Modeling Conundrums

Abstract

The mainstream research in interest-rate modeling has been focusing on a collection of risk tools and pricing formulas which are developed based on the simplified market assumptions and hypotheses. Despite the elegance of the structure, it is noticed that a crucial yet natural factor is missing: the relationship between curve-fitting algorithms and no-arbitrage restrictions on a bond portfolio. Also, the discrepancy between risk-free and default-free bonds is often ignored. This study discusses the modeling conundrums and proposes a framework based on the preferred-habitat hypothesis for advanced term-structure construction that overcomes these limitations in current models. This article serves as an introduction for future work.

Share and Cite:

Lin, P. (2014) Interest-Rate Modeling Conundrums. Journal of Mathematical Finance, 4, 328-332. doi: 10.4236/jmf.2014.45030.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Fisher, I. (1930) The Theory of Interest. Macmillan, New York.
[2] Harrison, J.M. and Pliska, S.R. (1981) Martingales and Stochastic Integrals in the Theory of Continuous Trading. Stochastic Processes and Their Applications, 11, 215-260.
http://dx.doi.org/10.1016/0304-4149(81)90026-0
[3] Geman, H., El Karoui, N. and Rochet, J.-C. (1995) Changes of Numéraire, Changes of Probability Measure and Option Pricing. Journal of Applied Probability, 32, 443-458.
http://dx.doi.org/10.2307/3215299
[4] Jarrow, R.A. (2009) The Term Structure of Interest Rates. Annual Review of Financial Economics, 2, 69-96.
http://dx.doi.org/10.1146/annurev.financial.050808.114513
[5] Culbertson, J. (1957) The Term Structure of Interest Rates. Quarterly Journal of Economics, 71, 485-517.
http://dx.doi.org/10.2307/1885708
[6] Modigliani, F. and Sutch, R. (1966) Innovations in Interest-Rate Policy. Interest-Rate Policy. American Economic Review, 56, 178-197.
[7] Filipovic, D. (2001) Consistency Problems for Heath-Jarrow-Morton Interest Rate Models. Springer, Berlin.
http://dx.doi.org/10.1007/b76888
[8] Krishnamurthy, A. and Vissing-Jorgensen, A. (2010) The Aggregate Demand for Treasury Debt. Working Paper.
[9] Duffee, G.R. (1996) Idiosyncratic Variation of Treasury Bill Yields. Journal of Finance, 51, 527-551.
http://dx.doi.org/10.1111/j.1540-6261.1996.tb02693.x
[10] Duffee, G.R. (1996) Special Repo Rates. Journal of Finance, 51, 493-526.
http://dx.doi.org/10.1111/j.1540-6261.1996.tb02692.x
[11] Heath, D., Jarrow, R. and Morton, A. (1992) Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation. Econometrica, 60, 77-105.
http://dx.doi.org/10.2307/2951677
[12] Bjork, T. (2009) Arbitrage Theory in Continuous Time. 3rd Edition, Oxford.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.