Optimal Exercise of Executive Stock Options and Implications for Valuation

The cost of executive stock options to shareholders has become a focus of attention in ̄nance and accounting. The di±culty is that the value of these options depends on the exercise policies of the executives. Because these options are nontransferable, the usual theory does not apply. We analyze the optimal exercise policy for a utility-maximizing executive and indicate when the policy is characterized by a critical stock price boundary. We provide a counterexample in which the executive exercises at low and high stock prices but not in between. We show how the policy varies with risk aversion, wealth, and volatility and explore implications for option value. For example, option value can decline as volatility rises. With the explosive growth of executive stock options in corporate compensation, the cost of these options to shareholders has become a focus of attention in ̄nance and accounting. Recent regulation requiring ̄rms to recognize option expense after 2005 has intensi ̄ed the demand for suitable valuation methods. The di±culty is that the value of these options depends crucially on the exercise policies of the option holders, but because these options are nontransferable, the usual theory does not apply. In the case of an ordinary call, the holder can sell the option at any time, so his goal is presumably to maximize the option's present value. The value-maximizing exercise policy in a Black-Scholes world has been researched extensively (see Merton (1973), Van Moerbeke (1976), Roll (1977), Geske (1979), Whaley (1981), Kim (1990)). It calls for exercising the option once the stock price rises above a critical level. This critical level is increasing in the riskless rate, the stock return volatility, and the time remaining to maturity, and it is decreasing in the dividend rate, with no early exercise if the dividend rate is zero. By contrast, the holder of an executive stock option must bear the risk of the option payo®, so simply maximizing the option's present value is generally not optimal. Indeed, evidence indicates that executives systematically exercise options on non-dividend paying stocks well before expiration. The executive presumably chooses an option exercise policy as part of a greater utility maximization problem that includes other decisions, such as portfolio and consumption choice and managerial strategy. This paper studies the optimal exercise policy for an executive stock option under simple but appealing assumptions about the executive's choice set. We address the questions of when the policy can be described by a critical stock price boundary, as in the case of an ordinary option, and how this boundary varies with executive risk aversion, wealth and stock price volatility. We then explore the implications for option value. The intuition that the need for diversi ̄cation can lead an executive to sacri ̄ce some option value by exercising it early is well understood in the literature, but explicit theory of the optimal exercise of ESOs is still developing. Huddart (1994), Marcus and Kulatilaka (1994), and Carpenter (1998) build binomial models of the utilitymaximizing exercise decision with exogenous assumptions about how non-option wealth is invested. Detemple and Sundaresan (1999) extend these to allow for simultaneous option exercise and portfolio choice decisions. These papers establish the economic approach to ESO valuation, focusing on the optimality of early exercise and the fact that this makes ESOs worth less than their Black-Scholes value rather than an in-depth analysis of the exercise policy itself. In a continuous-time framework, Ingersoll (2006) develops a subjective option valuation methodology assuming the option is a marginal component of the executive's portfolio. Kadam, Lakner, and Srinivasan (2003) and Henderson (2004) model the optimal exercise policy for an in ̄nite horizon option, but their models link the manager's consumption date to the option exercise date, which can distort the exercise decision, even in the absence of trading restrictions.