Date of Award

5-2010

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. Qiji J. Zhu

Second Advisor

Dr. Yuri S. Ledyaev

Third Advisor

Dr. Jay Treiman

Fourth Advisor

Dr. Deming Zhuang

Abstract

Pricing derivatives is one of the central issues in mathematical finance. The seminal work of Black, Scholes and Merton has been the cornerstone of option pricing since their introduction in 1973. Their work influenced the pricing theory of other derivatives as well.

This derivative pricing theory has two primary shortcomings. Firstly, the theoretical pricing in such theories are not accompanied by a stable trading strategy. Secondly, they often assume that the market agents use a uniform model for the underlying instrument and that the market prices of the derivatives reveal all the information about the underlying instrument.

Theoreticians like Grossman and Stiglitz have pointed out that market equilibrium models without considering the role of information dissemination, are often incomplete. On the other hand, traders like Soros, presented an empirical theory, called the theory of reflection, where he conjectures that a swing between a boom and a bust is the market norm.

The aim of this thesis is to develop the theoretical framework and conduct two carefully designed tests to demonstrate that the prevailing pricing techniques are too general to provide guidance for investment practice.

In the first part we provide evidence using a simple and well known trend tracking tool, that there is indeed inefficiencies in the option market that one can take advantage of. We also show that trading strategies that are stable under small model perturbations are those of pure positions like buying a call, writing a covered call, a vertical spread or pure stock.

In the other part, we focus on the class of optionable biomedical companies with small market capitalization and narrow product focus, which are known for having price jumps whose timings are predictable. We present evidence using an alternative model that it is possible to extract more accurate information on the price movement of the stock from the option prices.

Access Setting

Dissertation-Open Access

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Included in

Mathematics Commons

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