This thesis applies the concept of cost e ciency to the design of executive compensation. In a classical Black-Scholes framework, we are able to express the cost e cient counterpart of the Asian Executive Option explicitly, and design a payo that has the same distribution as the Asian Executive Indexed Option but comes at a cheaper price. The cost e cient counterpart of the latter option is not analytically tractable, but we are able to simulate its price. Furthermore, we extend the study of these two types of options in the presence of stochastic interest rates modeled by a Vasicek process. We are able to derive new closedform pricing formulas for these options. A framework for crafting the state price process is introduced. From here, an explicit expression for the state process is given and its distribution is derived. Using the pricing formulas and the state price process, we are then able to simulate the prices of the corresponding cost e cient counterparts in a stochastic interest rate environment. We conclude with some avenues for future research.

This thesis applies the concept of cost e ciency to the design of executive compensation. In a classical Black-Scholes framework, we are able to express the cost e cient counterpart of the Asian Executive Option explicitly, and design a payo that has the same distribution as the Asian Executive Indexed Option but comes at a cheaper price. The cost e cient counterpart of the latter option is not analytically tractable, but we are able to simulate its price. Furthermore, we extend the study of these two types of options in the presence of stochastic interest rates modeled by a Vasicek process. We are able to derive new closedform pricing formulas for these options. A framework for crafting the state price process is introduced. From here, an explicit expression for the state process is given and its distribution is derived. Using the pricing formulas and the state price process, we are then able to simulate the prices of the corresponding cost e cient counterparts in a stochastic interest rate environment. We conclude with some avenues for future research.