Cumulative prospect theory and its application in employee stock options and a consumption model

This thesis focuses on the concept of loss aversion in cumulative prospect theory and applies cumulative prospect theory to explain people's consumption behavior and the issuance of stock options to both employees and executives. Firstly, I provide a canonical way to frame loss aversion in cumulative prospect theory. I formally define an index of loss aversion as a function to reflect gain/loss comparisons. This index, different from the one defined by Kobberling and Wakker (2005), can be naturally 'used to fully describe the characteristics of loss aversion. With this index, equivalent conditions for loss aversion and strong loss aversion can be achieved. Distinctions of my definition from the previous ones are discussed in details. I also attempt to fit the special classes of utility functions into my definition. Compar- ative loss aversion can be defined through Yaari's acceptance sets and a standard asset ./ allocation problem. The conclusion is: the more loss averse an agent is, the smaller the acceptance set is and the less she will invest in risky assets. Secondly, I create a cumulative prospect theory multiperiod model to explain the fact that employees like to be paid with stock options. Essentially, it is the psycho- logical characteristic that people are prone to overweight the probability for extreme large returns to make the stock option preferred to the Black-Scholes price or the cost to the company, even when there is no optimism among employees. Employees'desire to hold options increases as firm volatility or optimism increases. My model is also consistent with other observed facts such as typical exercise behavior. Loss aversion in cumulative prospect theory can trigger early exercise behavior when the stock price is high, since the fear for a future drop of the stock price dominates the potential hap- piness brought by future gains. I also analyse the executive's compensation package. I find that a multiperiod risk averse model will predict a high base salary and some positive holdings in stock options in the optimal package as observed in the empirical research. Finally, I try to solve the puzzle about people's asymmetric reaction to the ex- pected income changes. I extend Kimball's two-period consumption model through incorporating the psychological utility function from prospect theory. Still within the expected utility framework, the asymmetric effect of loss aversion and the definition of reference level increase the flexibility of the model. Now the optimal consumption is determined by risk aversion and prudence in the general consumption utility, loss aversion, risk aversion and prudence on gains, and risk loving and anti-prudence on losses in the psychological utility. The most important findings are: for 'habit stickers', when they expect the future income to increase, they increase their current consump- tion synchronously, but when they expect a decrease for their future income, they may not lower their current living standards; for those with fully-adjusted reference levels, when they hear good news about the future income, they do not substantially increase today's consumption, and they are prone to lower their current living standards in front of bad news.EThOS - Electronic Theses Online ServiceGBUnited Kingdo