Sun, Jia, Ph.D. (2011) Models of executive stock options. PhD thesis, University of Warwick.

Abstract

This thesis presents novel utility indifference models to solve versions of problems faced by the executives compensated with periodical option grants in practice. Chapter 2 provides a comprehensive analysis of a single executive stock option (ESO). A closed-form solution to the exercise threshold instantaneously before maturity is obtained, and the leading driver of the slope of the exercise thresholds close to and far from maturity is identified. This Chapter forms the foundation for further investigation of more complex problems in later Chapters. Chapter 3 investigates the optimal exercise of a portfolio of ESOs with different strikes and maturities. This problem is particularly faced by the executives who receive option grants annually and over time cumulate a portfolio of options with different characteristics. We show that the optimal exercise order can switch endogenously, and the timing of this switch can change the exercise thresholds for a particular option and/or all options relative to a stand-alone basis, depending on their strikes and maturities. This makes the value and cost of the option portfolio lower than the sum of the values and costs for each individual option on a standalone basis. Therefore, one of the implications from Chapter 3 is that it can produce a more accurate method for valuing and accounting for a portfolio of ESOs. Furthermore, the empirical literature suggests that the Executive Stock Option Plans (ESOPs) are often into multi-year plans, and thus Chapter 4 considers the problem for an executive who anticipates receiving a new option grant in the future and has taken it into account as part of his portfolio. Since the future options are granted at-the-money, the strike price is stochastic ex ante. We show that the future option with a stochastic strike price can significantly affect the exercise strategy of the executive’s existing options, and thus change the cost of the existing options and the overall portfolio. Therefore, Chapter 4 can provide a method to recognise the cost of multi-year ESOPs. Lastly, another problem arising from granting ESOs periodically is that the executive can purposely time his new option grant in order to maximise the value of his option compensation. Since this issue has been well suggested by the empirical literature, Chapter 5 investigates this problem theoretically in the utility framework. Our model can identify the maximum benefit for the executive of timing his option awards and the cost of this to the firm. Our results are quite consistent with the empirical findings.

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