A Probabilistic Analysis of Autocallable Optimization Securities
Open Access
- Author:
- Samuel, Gilna K
- Graduate Program:
- Statistics
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- July 09, 2013
- Committee Members:
- Donald Richards, Thesis Advisor/Co-Advisor
- Keywords:
- Reverse Convertible Note
Autocallable Optimization Securities
Law of Total Expectation
Expected Net Payment
Fiduciary Duty - Abstract:
- We consider in this thesis some structured financial products, known as reverse convertible notes, which resulted in substantial losses to certain buyers of these notes in recent years. We shall focus on specific reverse convertible notes known as ``Autocallable Optimization Securities with Contingent Protection Linked to the S\&P 500 Financial Index'' because these notes are representative of the broad spectrum of reverse convertibles notes. Therefore, the analysis provided in this thesis can be applied to many other reverse convertible notes. In the early part of the thesis, we describe these reverse convertible notes. Further, we identify potential areas of confusion in the pricing supplement to the prospectus for these notes; hence, we deduce two possible interpretations of the payment procedure for the notes. Next, we apply the Law of Total Expectation to obtain a probabilistic analysis for each interpretation of the payment procedure for these notes, and we determine the corresponding expected net payments to note-holders under various scenarios for the financial markets. In each interpretation of the payment procedure, we show that note-holders were highly likely to suffer substantial losses. As a consequence, we infer that financial advisers who recommended purchases of these notes did not exercise {\emph{fiduciary duty}} to their clients. Indeed, the prospectus is sufficiently complex that financial advisers generally lacked the mathematical knowledge and expertise to understand the prospectus completely, hence did not have the greater knowledge and expertise that is required by a fiduciary relationship. Therefore, financial advisers simply were unable to exercise fiduciary duty and ultimately misguided their clients. We conclude that these reverse convertibles notes were designed by financial institutions to insure themselves, against significant declines in the equities markets, at the expense of note-holders.