Backdating Executive Option Grants - Nanyang Technological ...

where∂V∂Pis the CEO incentive, n is the number of options, and C is estimated cost of issuingoptions calculated by the BS model.In Figure 4, we assume that the CEO has initial wealth of $5,000,000 and 66% of his wealthis invested in the company stock, while varying incentive levels. The relative risk aversion isassumed to be two and the options are assumed to be held for ten years. The incentive isinterpreted as the change in the certainty equivalent values of n options for each $1 change in thestock price. The grant-date stock price is normalized to be $100. Shareholders are aimed toprovide managers with a certain incentive level. Without loss of generality, we set four differentlevels for incentive: $1,000, $2,000, $3,000, and $5,000. 14 The four lines in Figure 4 correspondto the four incentive levels, respectively.As illustrated in Figure 4, the minimum BS cost is usually achieved when the strike price isset to be less than the grant-date price. For example, the minimum cost to the shareholders toachieve the executive incentive level of $3,000 is to issue option grants with the strike price of75% of the grant-date price.The simulation results for a different range of model parameters are reported in Table 6. Therelative risk aversion coefficient is assumed to be either two or three. The CEO incentive levelchanges from $1,000 to $5,000. The proportion of the CEO’s wealth invested in the firm isassumed to be either 33%, 50%, or 66%. For a wide range of model parameter values, theoptimal strike price is lower than the grant-date price. This phenomenon is more evident for themanager who is more risk-averse and more under-diversified. For the same level of managerialincentive, shareholders can save compensation costs by optimally setting the strike price. Thepercentage of cost savings, relative to setting the strike price to the grant-date price of $100,14 These incentive levels are interpreted as if stock price at year T=10 increases by $1 dollar, the CEO’s certaintyequivalent value will increase by $1,000, $2,000, $3,000, and $5,000, respectively.22