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We build a dynamic capital structure model to study the link between systematic risk exposure and debt maturity, as well as their joint impact on the term structure of credit spreads. Our model allows for time variation and lumpiness in the maturity structure. Relative to short-term debt, long-term debt is less prone to rollover risks, but its illiquidity raises the costs of financing. The risk premium embedded in the bankruptcy costs causes firms with high systematic risk to favour longer debt maturity, as well as a more stable maturity structure over the business cycle. Pro-cyclical debt maturity amplifies the impact of aggregate shocks on the term structure of credit spreads, especially for firms with high leverage or high beta, and for firms with a large amount of long-term debt maturing when the aggregate shock arrives. However, endogenous maturity choice can also reduce and even reverse the effect of rollover risk on credit spreads. We provide empirical evidence for the model predictions on both debt maturity and credit spreads. JEL classification: G32, G33 Bank classification: Asset pricing; Debt managementRésumé À l'aide d'un modèle dynamique de la structure de capital, les auteurs étudient le lien entre l'exposition des entreprises au risque systématique et l'échéance de leur dette, ainsi que les incidences conjointes de ces deux facteurs sur la structure par terme des écarts de crédit. Dans leur modèle, la structure des échéances peut varier dans le temps et être irrégulière. Les obligations à long terme sont moins sensibles au risque de refinancement que les titres à court terme, mais leur illiquidité a pour effet d'alourdir les coûts d'emprunt. La prime de risque intégrée aux coûts de faillite amène les firmes très exposées au risque systématique à préférer une dette à plus long terme et une structure des échéances plus stable sur le cycle économique. La procyclicité des échéances amplifie les répercussions des chocs globaux sur la structure par terme des écarts de crédit, surtout dans le cas des entreprises fortement endettées ou dont les titres affichent un bêta élevé et de celles qui ont un volume considérable d'obligations à long terme échéant au moment du choc global. Cependant, le choix endogène de l'échéance peut également atténuer, voire inverser, les effets du risque de refinancement sur les écarts de crédit. Les auteurs testent empiriquement la validité des prévisions de leur modèle concernant l'échéance de la dette et les écarts de crédit.

We build a dynamic capital structure model to study the link between firms' systematic risk exposures and their time-varying debt maturity choices, as well as its implications for the term structure of credit spreads. Compared to short-term debt, long-term debt helps reduce rollover risks, but its illiquidity raises the costs of financing. With both default risk and liquidity costs changing over the business cycle, our calibrated model implies that debt maturity is pro-cyclical, firms with high systematic risk favor longer debt maturity, and that these firms will have more stable maturity structures over the cycle. Moreover, pro-cyclical maturity variation can significantly amplify the impact of aggregate shocks on the term structure of credit spreads, especially for firms with high beta, high leverage, or a lumpy maturity structure. We provide empirical evidence for the model predictions on both debt maturity and credit spreads.

PurposeThe purpose of this paper is to extend the models of Johnson and Stulz, Klein and Klein and lnglis to analyse the properties of vulnerable American options.Design/methodology/approachThe presented model allows default prior to the maturity of the option based on a barrier which is linked to the payoff on the option. Various measures of risk denoted by the standard Greek letters are studied, as well as additional measures that arise because of the vulnerability.FindingsThe paper finds that the delta of a vulnerable American put does not always increase with the price of the underlying asset, and may be significantly smaller than that of a non‐vulnerable put. Because of deadweight costs associated with bankruptcy, delta and gamma are undefined for some values of the underlying asset. Rho may be considerably higher while vega may be smaller than for non‐vulnerable options. Also, the probability of early exercise for vulnerable American options is higher and the price of the underlying asset at which this is optimal depends on the degree of credit risk of the option writer.Originality/valueThis paper makes a contribution to understanding the effect of credit risk on option valuation.

Bank of Canada working papers are theoretical or empirical works-in-progress on subjects in economics and finance. The views expressed in this paper are those of the authors. No responsibility for them should be attributed to the Bank of Canada.

A high-frequency longitudinally driven giant magnetoimpedance (GMI) effect has been measured in stress-annealed Fe73Cu1Nb1.5V2Si13.5B9 nanocrystalline ribbons. Based on how the impedance phase varies with the external magnetic field, it becomes clear that the imaginary part of the complex permeability, μ″, which is related to magnetic losses, plays an important role in the high-frequency longitudinally driven GMI effect. The transverse anisotropy field Hk can be readily determined by a sharp minimum in the curve of the impedance phase as a function of the external magnetic field. This provides a new method for measuring the magnetic anisotropy field in such systems.

Key indicatorsSingle-crystal X-ray study T = 293 K Mean (C-C) = 0.005 Å R factor = 0.037 wR factor = 0.081 Data-to-parameter ratio = 15.7For details of how these key indicators were automatically derived from the article, see

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