The Stock Options Value To The Executive

One of fundamental problems in modern finance theory is the capi-tal asset pricing. The fundamental assumptions in the standard financialtheory are the rational hapothsis and the expectation utility assumption,and both of them are the foundation of several well-known economic the-ories, say, CAPM, MM and B-S option pricing. In order to pricing thecapital asset, one simple approach is to estimate its future value andtake their expectation as the valuation of this asset. Since 1970's in lastcentury, the problems on optimal investment and capital asset pricingappeal to more and more research interests from academic society andfinancial industries. The financial theory on complete market has beenfully developed. However, these researches simplify the theory of condi-tions, which inconsistent with the financial markets, thus being unableto satisfy the request in the application.This paper is devoted to the cap-ital asset pricing in incomplete financial market, focused on the utilityindifference pricing, therefore, the purpose of this paper become moresignificant.This paper is structured as follows. In chapter 1 , some basis knowl-edge is given. We begin by introduction executive compensation andstock options. The next section, a brief review of utility function isgiven. We introduce utility indifference pricing and give a survey ofthe literature in chapter2. In chapter 3,we make a short review on thestock options. Our review follows the order of the above research design.The main result of this paper is given in chapter 4. I set up a con-tinuous time utility maximization model to value the stock and optioncompensations to the executive receiving it. I use the power utility tocompute the value to the executive and derive an approximately solution. Theorem2:Forh(S_T)≥0 and h not bounded above , the utility functionof executive is U(x) =(x^1-R)/(1-R),(R≠1),the time t price p ofλunits ofh(S_T), given a current wealth x , then the reservation price to theexecutive is...