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

Alexander Veremyev (), Peter Tsyurmasto (), Stan Uryasev () and R. Rockafellar ()

Computational Management Science, 2014, vol. 11, issue 4, 364 pages

Abstract: 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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: OR banking; Convex optimization; Convex-concave-convex probability distribution; Implied copula; CDO pricing; 90 (Operations Research; Mathematical Programming) (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10287-013-0176-4 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:comgts:v:11:y:2014:i:4:p:341-364

Ordering information: This journal article can be ordered from
http://www.springer. ... ch/journal/10287/PS2

DOI: 10.1007/s10287-013-0176-4

Access Statistics for this article

Computational Management Science is currently edited by Ruediger Schultz

More articles in Computational Management Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().