×

Term structure models with parallel and proportional shifts. (English) Zbl 1186.91187

Summary: The paper investigates the possibility of an arbitrage-free model for the term structure of interest rates where the yield curve only changes through a parallel shift. HJM type forward rate models driven by a multidimensional Wiener process and by a general marked point process are considered. Within this general framework it is shown that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. It is also shown that there exists no nontrivial flat term structure model. The same analysis is repeated for a similar case, in which the yield curve only changes through proportional shifts.

MSC:

91G10 Portfolio theory
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Armerin F., Aspects of cash flow valuation (2004) · Zbl 1401.91549
[2] Babbs S., Mathematics at Derivative Securities pp 394– (1997)
[3] DOI: 10.2307/2330253 · doi:10.2307/2330253
[4] DOI: 10.2469/faj.v39.n4.15 · doi:10.2469/faj.v39.n4.15
[5] DOI: 10.1111/1467-9965.00072 · Zbl 0980.91030 · doi:10.1111/1467-9965.00072
[6] DOI: 10.1111/1467-9965.00031 · Zbl 0884.90014 · doi:10.1111/1467-9965.00031
[7] DOI: 10.1111/1467-9965.00113 · Zbl 1055.91017 · doi:10.1111/1467-9965.00113
[8] Boyle P. P., Journal of the Institute of Actuaries 105 pp 177– (1978)
[9] DOI: 10.1111/1467-9965.00028 · Zbl 0884.90008 · doi:10.1111/1467-9965.00028
[10] DOI: 10.3905/jpm.1994.409472 · doi:10.3905/jpm.1994.409472
[11] Dempster M, Mathematics of Derivative Securities (1997)
[12] Filipović D., Consistency Problems for Heath-Jarrow-Morton Interest Rate Models (2001) · Zbl 1008.91038 · doi:10.1007/b76888
[13] DOI: 10.1016/S0022-1236(03)00008-9 · Zbl 1013.60035 · doi:10.1016/S0022-1236(03)00008-9
[14] DOI: 10.1086/295402 · doi:10.1086/295402
[15] DOI: 10.2307/2951677 · Zbl 0751.90009 · doi:10.2307/2951677
[16] DOI: 10.1016/S0167-6687(02)00158-0 · Zbl 1074.91016 · doi:10.1016/S0167-6687(02)00158-0
[17] DOI: 10.2307/2330468 · doi:10.2307/2330468
[18] Jacod J., Limit Theorems for Stochastic Processes (1987) · doi:10.1007/978-3-662-02514-7
[19] Macaulay, F. 1938. ”Some theoretical problems suggested by the movements of interest rates, bond yields, and stock prices in the U.S. since 1856”. NBER, New York, USA
[20] Milgrom P. R., Transactions of the Society of Actuaries 37 pp 241– (1985)
[21] DOI: 10.1016/0167-6687(91)90005-I · Zbl 0754.90002 · doi:10.1016/0167-6687(91)90005-I
[22] Redingtion F., Journal of the Institute of Actuaries 78 pp 286– (1952)
[23] DOI: 10.1016/0167-6687(90)90030-H · Zbl 0721.62104 · doi:10.1016/0167-6687(90)90030-H
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.