Polynomial upper and lower bounds for financial derivative price functions under regime-switching

Louis Bhim and Reiichiro Kawai

Journal of Computational Finance

Abstract: We present a new approach to bounding financial derivative prices in regime-switching market models from both above and below. We derive sufficient conditions under which a particular class of functions act as bounds for the prices of financial derivatives in regime-switching market models. Using these sufficient conditions, we then formulate, in a general setting, optimization problems whose solutions can be identified with tight upper and lower bounds. The problems are made numerically tractable by imposing polynomial structures and employing results from the theory of sum-of-squares polynomials to arrive at a semidefinite programming problem that is implementable by existing software. The bounds obtained take the form of smooth polynomial functions and are valid for a continuous range of initial times and states. Moreover, they are obtained without recourse to sample path simulation or discretization of the temporal or spatial variables. We demonstrate the effectiveness of the proposed method on European-, barrier- and American-style options in several regime-switching settings with and without jumps.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-of-computational-fina ... der-regime-switching (text/html)

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:rsk:journ0:5940526

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine (maintainer@infopro-digital.com).