Asymptotics of the price oscillations of a European call option in a tree model

Francine Diener and Diener Marc

Mathematical Finance, 2004, vol. 14, issue 2, 271-293

Abstract: It is well known that the price of a European vanilla option computed in a binomial tree model converges toward the Black‐Scholes price when the time step tends to zero. Moreover, it has been observed that this convergence is of order 1/n in usual models and that it is oscillatory. In this paper, we compute this oscillatory behavior using asymptotics of Laplace integrals, giving explicitly the first terms of the asymptotics. This allows us to show that there is no asymptotic expansion in the usual sense, but that the rate of convergence is indeed of order 1/n in the case of usual binomial models since the second term (in ) vanishes. The next term is of type C2(n)/n, with C2(n) some explicit bounded function of n that has no limit when n tends to infinity.

Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

Downloads: (external link)
https://doi.org/10.1111/j.0960-1627.2004.00192.x

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:bla:mathfi:v:14:y:2004:i:2:p:271-293

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0960-1627

Access Statistics for this article

Mathematical Finance is currently edited by Jerome Detemple

More articles in Mathematical Finance from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().