Thursday, May 28, 2020 | 12:00 pm | Zoom

Title: On Stochastic Dominance Option Bounds in Discrete and Continuous Space and Time with Stochastic and Deterministic Volatility with Constant Relative Risk Aversion

Abstract

This thesis makes original contributions to the field of asset pricing, which is a field dedicated to describing the prices of financial instruments and their characteristics. The prices of these financial instruments are determined by the behavior of investors who buy and sell them, and so asset pricing is ultimately done by modeling the behavior of investors. One method for achieving this is through the framework of stochastic dominance. This thesis specifically deals with a specific class of financial instruments called European options and reviews the literature on stochastic dominance option pricing and discusses new methods for finding stochastic dominance bounds on options in both discrete and continuous time under both deterministic and stochastic volatility. The results presented here extends the works of Ritchken and Kuo (1988) and Perrakis and Ryan (1984). Furthermore, stochastic dominance bounds for Heston’s (1993) stochastic volatility model are obtained under certain assumptions. Finally, this thesis extends the work of Carr and Madan (1999) and solves for the characteristic function of the call price given the physical characteristic function under the CRRA utility model.

Advisor: Dr. Wojbor Woyczynski

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