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Non-convexity of the optimal exercise boundary for an American put option on a dividend-paying asset

Cheng, Huibin (2011) Non-convexity of the optimal exercise boundary for an American put option on a dividend-paying asset. Doctoral Dissertation, University of Pittsburgh.

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    Abstract

    In this thesis, we prove that the optimal exercise boundary of the American put option is not convex when the dividend rate of the underlying assetwhich follows a geometric Brownian motion, is slightly larger than the risk-free interest rate. We show that the non-convex region occurs very near the expiry time. Numerical evidence is also provided which suggests that the convexity of the optimal exercise boundary is restored when the dividend rate is sufficiently larger than the interest rate. In addition we provide the near-expiry and far-from-expiry behavior of the boundary. To complete the rigorous proofs, we also show that the optimal exercise boundary has $C^infty$ regularity.


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    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmail
    Committee ChairChadam, Johnjohn.chadam@gmail.com
    Committee CoChairChen, Xinfuxinfu@pitt.edu
    Committee MemberRichard, Jean-Francoisfantin@pitt.edu
    Committee MemberManfredi, Juan J.manfredi@pitt.edu
    Committee MemberLayton, William J.wjl@pitt.edu
    Title: Non-convexity of the optimal exercise boundary for an American put option on a dividend-paying asset
    Status: Unpublished
    Abstract: In this thesis, we prove that the optimal exercise boundary of the American put option is not convex when the dividend rate of the underlying assetwhich follows a geometric Brownian motion, is slightly larger than the risk-free interest rate. We show that the non-convex region occurs very near the expiry time. Numerical evidence is also provided which suggests that the convexity of the optimal exercise boundary is restored when the dividend rate is sufficiently larger than the interest rate. In addition we provide the near-expiry and far-from-expiry behavior of the boundary. To complete the rigorous proofs, we also show that the optimal exercise boundary has $C^infty$ regularity.
    Date: 16 September 2011
    Date Type: Completion
    Defense Date: 11 May 2011
    Approval Date: 16 September 2011
    Submission Date: 12 May 2011
    Access Restriction: No restriction; Release the ETD for access worldwide immediately.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-05122011-151701
    Uncontrolled Keywords: American put option; early exercise boundary; non-convexity
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:44
    Last Modified: 10 Feb 2012 11:29
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-05122011-151701/, etd-05122011-151701

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