Essays on stock price behavior and options

Abstract

This paper provides three essays on stock price behavior and options. The first chapter suggests that stable distribution is related to the phenomena of intermediate term momentum and long term reversal. Although there are several papers about non-normality of financial data, normal distribution is still the most popular distribution, which can lead overuse of normal distribution and misunderstanding the nature of financial data. Or frequent occurrence of extreme events can make momentum. The second chapter derives approximate valuation formulas for basket options and Asian options under the jump-diffusion process. To obtain an approximation for options prices under the jump-diffusion process, we extend the Taylor expansion method developed by Ju (2002) under the diffusion process. We show that the Taylor expansion method suggested in this paper provides the best pricing performance among log-normal, four-moment, and Taylor expansion approximations, in general. The performance improvement using the Taylor expansion method increases as time to maturity increases. In addition, accounting for jump effects becomes important when jumps are asymmetric. The final chapter provides that the executive’s incentives to increase the stock price can be very low on some ranges of the stock price. So we propose a new stock option compensation whose payoffs are concave with respect to the stock price when the stock price at option’s maturity exceeds the strike price. This kind of options allows the executive to have greater incentives compared with the traditional option model. In addition, the incentives at some time (after the grant date) might not be optimal even though the firm chose the moneyness of the option that gave the executive the optimal incentives on the grant date.