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The Relationship Between Risk and Maturity In A Stochastic Setting
Author(s) -
Zipkin Paul H.
Publication year - 1992
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1992.tb00024.x
Subject(s) - maturity (psychological) , interest rate , bond , economics , econometrics , interest rate risk , zero coupon bond , markov chain , sensitivity (control systems) , coupon , short rate , financial economics , yield curve , actuarial science , monetary economics , mathematics , statistics , finance , psychology , developmental psychology , electronic engineering , engineering
This paper explores the interest rate sensitivity of the prices of bonds and other securities when the instantaneous interest rate follows a Markov process. We show that whenever the interest rate describes a diffusion process the sensitivity of zero‐coupon bonds increases with maturity. More generally, we characterize the risk‐maturity relationship for contingent claims. This investigation yields a new property of option prices in the case where the underlying security price is a diffusion.