American Options

Norbert Hilber, Oleg Reichmann, Christoph Schwab and Christoph Winter
Additional contact information
Norbert Hilber: Zurich University of Applied Sciences
Oleg Reichmann: Swiss Federal Institute of Technology (ETH)
Christoph Schwab: Swiss Federal Institute of Technology (ETH)
Christoph Winter: Allianz Deutschland AG

Chapter Chapter 5 in Computational Methods for Quantitative Finance, 2013, pp 65-74 from Springer

Abstract: Abstract Pricing American contracts requires, due to the early exercise feature of such contracts, the solution of optimal stopping problems for the price process. Similar to the pricing of European contracts, the solutions of these problems have a deterministic characterization. Unlike in the European case, the pricing function of an American option does not satisfy a partial differential equation, but a partial differential inequality, or to be more precise, a system of inequalities. We consider the discretization of this inequality both by the finite difference and the finite element method where the latter is approximating the solutions of variational inequalities. The discretization in both cases leads to a sequence of linear complementarity problems (LCPs). These LCPs are then solved iteratively by the PSOR algorithm. Thus, from an algorithmic point of view, the pricing of an American option differs from the pricing of a European option only as in the latter we have to solve linear systems, whereas in the former we need to solve linear complementarity problems.

Keywords: Variational Inequality; Option Price; Linear Complementarity Problem; American Option; European Contract (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:sprfcp:978-3-642-35401-4_5

Ordering information: This item can be ordered from
http://www.springer.com/9783642354014

DOI: 10.1007/978-3-642-35401-4_5

Access Statistics for this chapter

More chapters in Springer Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().