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(Unpublished)
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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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| 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: |
http://etd.library.pitt.edu/ETD/available/etd-05122011-151701/, etd-05122011-151701 |
| Date Deposited: |
10 Nov 2011 19:44 |
| Last Modified: |
15 Nov 2016 13:43 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/7857 |
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