Monte Carlo Methods for Pricing Discrete Parisian Options

European Journal of Finance, Vol. 17, Issue 3, 2011

40 Pages Posted: 11 Jul 2009 Last revised: 24 Jan 2012

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Phelim P. Boyle

Wilfrid Laurier University - School of Business & Economics; University of Waterloo

Date Written: June 16, 2009

Abstract

The paper develops an efficient Monte Carlo method to price discretely monitored Parisian options based on a control variate approach. The paper also modifies the Parisian option design by assuming the option is exercised when the barrier condition is met rather than at maturity. We obtain formulas for this new design when the underlying is continuously monitored and develop an efficient Monte Carlo method for the discrete case. Our method can also be used for the case of multiple barriers. We use numerical examples to illustrate the approach and reveal important features of the different types of options considered. Some performance-based executive stock options include different tranches of discretely monitored Parisian options and we illustrate this with a practical example.

Keywords: Parisian Options, Monte Carlo, Discrete Monitoring, Control Variate, Early Exercise, Executive Stock Options, Mr. Thain.

JEL Classification: G13

Suggested Citation

Bernard, Carole and Boyle, Phelim P., Monte Carlo Methods for Pricing Discrete Parisian Options (June 16, 2009). European Journal of Finance, Vol. 17, Issue 3, 2011, Available at SSRN: https://ssrn.com/abstract=1420761

Carole Bernard (Contact Author)

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Phelim P. Boyle

Wilfrid Laurier University - School of Business & Economics ( email )

Waterloo, Ontario N2L 3C5
Canada
519 884 1970 (Phone)
519 888 1015 (Fax)

University of Waterloo

Waterloo, Ontario N2L 3G1
Canada

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