Asymptotic behaviour of random maturity barrier options

Nawel Khodja, Faouzi Trabelsi and Mohamed Riad Remita

International Journal of Operational Research, 2016, vol. 26, issue 2, 221-235

Abstract: In this paper, we study and analyse European barrier options in the Black-Scholes framework with deterministic or random maturity. When the maturity is deterministic, we provide closed form formulas for (up and out) European barrier call and put options. When the maturity is random, we suppose that it follows a Poisson distribution. In this case, we provide an explicit expression for the European barrier call option, presented in the form of a numerical series. In order to make our results more explicit, we give a Taylor expansion's formula for the random maturity European barrier call option, as the volatility decreases to zero. Since there are no, or at least, it is hard to obtain closed-form formulas for random maturity barrier contingent claims, the last formula should be very useful both in practice and theory of option pricing.

Keywords: option pricing; hitting time; random maturity; deterministic maturity; European barrier call; European barrier put; up and out barrier option; small volatility; Taylor expansion; asymptotic behaviour; European barrier options; Black-Scholes. (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.inderscience.com/link.php?id=76302 (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:ids:ijores:v:26:y:2016:i:2:p:221-235

Access Statistics for this article

More articles in International Journal of Operational Research from Inderscience Enterprises Ltd
Bibliographic data for series maintained by Sarah Parker ().