The values and incentive effects of options on the maximum or the minimum of the stock prices and market index

In this study, we employ the certainty equivalent principle to investigate cost efficiency and incentives of the options on the maximum or the minimum of the stock prices and market index levels. In addition, the options with averaging features are also considered. Numerical results show that options on the maximum are more cost efficient and incentive-efficient than traditional ones. As for options on the minimum, they are more cost efficient than traditional ones only when the weight in the options is not very large. However, options on the minimum also provide stronger incentives to increase stock prices than traditional ones.