Research On Pricing Of Two Kinds Of Manager Stock Option

With the development of Principal Agent Theory, a new approach to company which con-trols the manager’s agency cost has been proposed, namely employee stock options. It was used to encourage the executives for a long period. Practice has proved that Stock Option was effec-tive measures on attracting, keeping and encouraging workers and to improve the productivity. The research of pricing of employee stock options is considerable realistic significance for the development of employee stock options in our country.This paper mainly study the pricing of two lypcs of employ slock options. One is the pricing of employ slock options with a barrier feature, and stock and financial index follow Browiiian motion:However a number of research indicated that the finance market doesn’t follow Brownian motion, but obeys more general fractional Brownian motion, so we study the indifference price of employ stock option under the situation which corporate stocks and financial index follow fractional Brownian motion, when we consider reset employ stock option. Because employee stock options are non-tradeable, the employee can’t trade corporate stocks, we apply utility-indifference valuation. In order to hedge the position, we let the employee invest the financial index, which is correlated with corporate stocks. Firstly, we define the value function as the maximal expectation of the utility. Secondly, deriving the associat-ed Hamilton-Jacobi-Reliman(HJB) equation by means of dynamic programming principal and stochastic control theory. Lastly, the pricing formulae of employee stock option for the valuation are obtained by Green’s function and a numerical analysis is made to illustrate the result.