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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. (Unpublished)

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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
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Cheng, Huibinhuc12@pitt.eduHUC12
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChadam,
Committee CoChairChen, Xinfuxinfu@pitt.eduXINFU
Committee MemberRichard, Jean-Francoisfantin@pitt.eduFANTIN
Committee MemberManfredi, Juan J.manfredi@pitt.eduMANFREDI
Committee MemberLayton, William J.wjl@pitt.eduWJL
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.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: American put option; early exercise boundary; non-convexity
Other ID:, etd-05122011-151701
Date Deposited: 10 Nov 2011 19:44
Last Modified: 15 Nov 2016 13:43


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