Calibrating probability distributions with convex-concave-convex functions: application to CDO pricing

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• 作者：Alexander Veremyev (1) (2)
  Peter Tsyurmasto (3)
  Stan Uryasev (3)
  R. Tyrrell Rockafellar (4)
  
• 关键词：OR banking ; Convex optimization ; Convex ; concave ; convex probability distribution ; Implied copula ; CDO pricing ; 90 (Operations Research ; Mathematical Programming)
• 刊名：Computational Management Science
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：11
• 期：4
• 页码：341-364
• 全文大小：634 KB
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• 作者单位：Alexander Veremyev (1) (2)
  Peter Tsyurmasto (3)
  Stan Uryasev (3)
  R. Tyrrell Rockafellar (4)
  
  1. Department of ISE, University of Florida, P.O. Box 116595, 303 Weil Hall, Gainesville, FL, 32611-6595, USA
  2. National Research Council/ Air Force Research Laboratory, Munitions Directorate, 101 W. Eglin Blvd, Eglin AFB, FL, 32542, USA
  3. Department of ISE, University of Florida, Risk Management and Financial Engineering Lab, P.O. Box 116595, 303 Weil Hall, Gainesville, FL, 32611-6595, USA
  4. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA
  
• ISSN：1619-6988

文摘

This paper considers a class of functions referred to as convex-concave-convex (CCC) functions to calibrate unimodal or multimodal probability distributions. In discrete case, this class of functions can be expressed by a system of linear constraints and incorporated into an optimization problem. We use CCC functions for calibrating a risk-neutral probability distribution of obligors default intensities (hazard rates) in collateral debt obligations (CDO). The optimal distribution is calculated by maximizing the entropy function with no-arbitrage constraints given by bid and ask prices of CDO tranches. Such distribution reflects the views of market participants on the future market environments. We provide an explanation of why CCC functions may be applicable for capturing a non-data information about the considered distribution. The numerical experiments conducted on market quotes for the iTraxx index with different maturities and starting dates support our ideas and demonstrate that the proposed approach has stable performance. Distribution generalizations with multiple humps and their applications in credit risk are also discussed.