A General Treatment of Barrier Options

66 Pages Posted: 26 Sep 1998  

Alessandro Sbuelz

Catholic University of Milan - Department of Mathematics, Quantitative Finance, and Econometrics; Bocconi University - CAREFIN - Centre for Applied Research in Finance

Abstract

This article offers a general unifying treatment of barrier options. The unifying treatment is based on a general representation of the risk-neutral density of the absorbed return process of the underlying asset: the "convolution density." On the basis of the convolution density, the article establishes relationships between plain and barrier options as well as knock-outs and knock-ins: the "plain/knock parities." The plain/knock parities provide new static hedging strategies for the replication of double barrier options; a double barrier option is a portfolio of single barrier options. The article then derives new representations for the analytical solution of option prices in the double barrier setting. For the first time, the analytical solution of the price of the contract with a single knock-in triggering a single knock-out is offered, and new representations of the analytical solution of the price of double knock-ins and knock-outs are also offered. The form of these analytical solutions is a series which absolutely converges at a very high rate.

JEL Classification: G13

Suggested Citation

Sbuelz, Alessandro, A General Treatment of Barrier Options. Available at SSRN: https://ssrn.com/abstract=103772 or http://dx.doi.org/10.2139/ssrn.103772

Alessandro Sbuelz (Contact Author)

Catholic University of Milan - Department of Mathematics, Quantitative Finance, and Econometrics ( email )

largo A. Gemelli 1
I-20123 Milan
Italy
+39 02 7234 2345 (Phone)
+39 02 7234 2671 (Fax)

HOME PAGE: http://ppd.unicatt.it/docenti/alessandro_sbuelz

Bocconi University - CAREFIN - Centre for Applied Research in Finance

Via Sarfatti, 25
Milan, 20136
Italy

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