[PAST EVENT] Applied Science Dissertation Defense - Sean Tarter [Zoom]
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PH.D. DISSERTATION DEFENSE: Three Essays in Financial Economics by Sean Tarter, PhD Candidate in Applied Science
ABSTRACT: Many models of asset behavior rely heavily upon no-arbitrage principles, which presume the absence of instantaneous risk-free profits throughout the market. The Essays in this Dissertation reconsider the plausibility of this assumption from three different perspectives and explore the potential implications of arbitrage as a generative market mechanic. The first essay examines dynamic hedging in the seminal works of (Black & Scholes, 1973; Merton, 1973) through the lens of the investor's purchasing power across involved assets. It is demonstrated that the budget set of their hedged portfolio will always be subject to a stochastic factor that cannot be hedged by their original approach. The second essay examines the commonly accepted assumption of the absence of static arbitrage in markets. Although the condition may frequently hold in approximation, any specific no-static arbitrage state is demonstrated to be an unstable solution, even in a simplified model of liquid option markets. This is a key result, since static arbitrages are not model-dependent. Given this instability, a reversal of many traditional approaches is adopted: Static arbitrage is modeled explicitly as a propulsive force for option price changes without presuming universal convergence. The result is a non-deterministic family of likely system trajectories, subject to a tuning parameter for price elasticities. The third essay revisits the works of (Black & Scholes, 1973; Merton, 1973), and their modeling methodology is placed within a more realistic market topology. This topology ubiquitously endows contracts with additional properties that are mathematically demonstrated to nullify the original hedging approach. After adopting the dynamics of the original works for the conversion terms of the embedded option, nullification is shown to occur even when investors attempt to exploit the properties of the new topological connections for hedging purposes or for model-dependent arbitrage. This new result is considered from the perspective of an institutional investor and relevant stochastic partial differential equations are derived for the appropriate representational basis.
MEETING INFORMATION [Zoom]
Nov 17, 2021, 2.00 pm EST
Zoom Meeting Meeting ID: 918 2165 1878
This is a public event.