Award Date

5-1-2012

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Michael D. Marcozzi

Second Committee Member

Chih-Hsiang Ho

Third Committee Member

Hongtao Yang

Fourth Committee Member

Seungmook Choi

Number of Pages

98

Abstract

Valuation of financial derivatives subject to liquidity risk remains an open problem in finance. This dissertation focuses on the valuation of European-style call option under limited market liquidity through the dynamic management of a portfolio of assets. We investigate liquidity from three perspectives: market breadth, depth, and immediacy. We present a general framework of valuation based on the optimal realization of a performance index relative to the set of all feasible portfolio trajectories. Numerical examples are then presented and analyzed that show option price increases as the market transitions from liquid to less liquid state. Furthermore, buying and selling activities, based on our optimal trading strategy, decrease as the market becomes less liquid because the gain from more frequent rebalancing of the portfolio is not able to offset the liquidity risk.

Keywords

Corporations – Valuation; Hamilton-Jacobi Equations; Liquidity (Economics); Option; Securities industry; Stock exchanges

Disciplines

Finance | Mathematics | Partial Differential Equations | Portfolio and Security Analysis

Language

English


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