{"title":"Monotonicity of the collateralized debt obligations term structure model","authors":"M. Barski","doi":"10.1080/17442508.2013.879145","DOIUrl":null,"url":null,"abstract":"The problem of existence of arbitrage-free and monotone collateralized debt obligations term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath–Jarrow–Morton–Musiela equation for the -forward rates with the use of the Milian-type result are formulated. Two state spaces are taken into account – of square integrable functions and a Sobolev space. For the first the regularity results concerning pointwise monotonicity are proven. Arbitrage-free and monotone models are characterized in terms of the volatility of the model and characteristics of the driving Lévy process.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2014-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics-An International Journal of Probability and Stochastic Processes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17442508.2013.879145","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
The problem of existence of arbitrage-free and monotone collateralized debt obligations term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath–Jarrow–Morton–Musiela equation for the -forward rates with the use of the Milian-type result are formulated. Two state spaces are taken into account – of square integrable functions and a Sobolev space. For the first the regularity results concerning pointwise monotonicity are proven. Arbitrage-free and monotone models are characterized in terms of the volatility of the model and characteristics of the driving Lévy process.
期刊介绍：
Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects.
Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly.
In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.
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