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Numerical Study of the Convexity of the Exercise Boundary of the American Put Option on a Dividend-Paying Asset

Chakraborty, Debapriti (2009) Numerical Study of the Convexity of the Exercise Boundary of the American Put Option on a Dividend-Paying Asset. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

Numerical evidence is provided to show that the optimal exercise boundary for American put options with continuous dividend rate d is convex for values d less than or equal to r, where r is the risk-free rate. For d greater than r, the boundary is not convex. As d increases beyond r, the non-convex region moves away from expiry and increases in size. A front-fixing method has been used to transform the American put problem into a nonlinear parabolic differential equation posed on a fixed domain. Explicit and implicit finite-difference methods are used to simulate the problem numerically. As a test, both the explicit and implicit method has been compared and the finite-difference methods give stable results.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Chakraborty, Debapritidebapriti@gmail.com
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChadam, John Mchadam@pitt.eduCHADAM
Committee MemberManfredi, Juan Jmanfredi@pitt.eduMANFREDI
Committee MemberLayton, William Jwjl@pitt.eduWJL
Date: 15 January 2009
Date Type: Completion
Defense Date: 2 December 2008
Approval Date: 15 January 2009
Submission Date: 11 December 2008
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: american put option; black-scholes equation; convexity; dividend; early exercise boundary; explicit; front fixing method; implicit; matlab; newton-raphson method; numerical methods
Other ID: http://etd.library.pitt.edu/ETD/available/etd-12112008-002727/, etd-12112008-002727
Date Deposited: 10 Nov 2011 20:10
Last Modified: 15 Nov 2016 13:54
URI: http://d-scholarship.pitt.edu/id/eprint/10314

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