Pricing Discretely Monitored Barrier Options by a Markov Chain

Posted: 8 Oct 2013

See all articles by Jin-Chuan Duan

Jin-Chuan Duan

National University of Singapore (NUS) - Business School and Risk Management Institute

Evan Dudley

Queen's University - Smith School of Business

Geneviève Gauthier

HEC Montreal - Department of Decision Sciences; HEC Montreal - Department of Management Sciences

Jean-Guy Simonato

HEC Montréal

Date Written: August 1, 2003

Abstract

The method here to price discretely monitored barrier options in both constant and time-varying volatility valuation frameworks uses a time-homogeneous Markov chain to approximate the underlying asset price process. It provides a natural framework for this pricing process because the discrete time step of the Markov chain can be easily matched with the monitoring frequency of the barrier. The underlying asset price can also be partitioned so as to place the barrier suitably. The method can efficiently handle difficult cases where the barrier is close to the initial asset price. Examples include both knock-in and knock-out barrier options. Different types of barriers such as single, double, and moving barriers are also analyzed.

Keywords: Barrier option, Markov chain

JEL Classification: G13

Suggested Citation

Duan, Jin-Chuan and Dudley, Evan and Gauthier, Genevieve and Simonato, Jean-Guy, Pricing Discretely Monitored Barrier Options by a Markov Chain (August 1, 2003). Journal of Derivatives, Vol. 10, 2003. Available at SSRN: https://ssrn.com/abstract=2337176

Jin-Chuan Duan

National University of Singapore (NUS) - Business School and Risk Management Institute ( email )

1 Business Link
Singapore, 117592
Singapore

Evan Dudley (Contact Author)

Queen's University - Smith School of Business ( email )

Goodes Hall
Kingston, Ontario K7L 3N6
Canada

Genevieve Gauthier

HEC Montreal - Department of Decision Sciences ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada

HEC Montreal - Department of Management Sciences ( email )

Montreal, Quebec H3T 2A7
Canada

Jean-Guy Simonato

HEC Montréal ( email )

3000, chemin de la Cote-Sainte-Catherine
Service de l'enseignement de la finance
Montreal, Quebec H3T 2A7
Canada
514-340-6807 (Phone)
514-340-5632 (Fax)

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