Employee stock options: much more valuable than you thought

Previous papers have argued that trading restrictions can result in a typical employee stock option having a subjective value (certainty equivalent value) that is substantially less than its Black-Scholes value. However, these analyses ignore the manager's ability to (at least partially) control the risk level within the firm. In this paper, we show how managerial control can lead to such options having much larger certainty equivalent values for employees who can exercise control. We also show that the potential for early exercise is substantially less valuable with managerial control. The certainty equivalent value for a European option with managerial control can easily exceed the Black-Scholes value for a comparable option without control. However, it is questionable whether Black-Scholes is an appropriate benchmark for an option where the underlying process exhibits controlled volatility. We show how to obtain a risk-neutral valuation for such an option. That risk-neutral value can be substantially greater or less than the Black- Scholes value. Furthermore, the option's certainty equivalent value can also be greater or less than its risk-neutral value

Heterogeneous Expectations, Short Sales Regulation and the Risk Return Relationship

L'étude traite de l'effet de la réglementation des ventes à découvert sur la relation rendement-risque, au Canada. ¸ partir du cadre développé par Jarrow (1980), nous développons une expression de la relation rendement-risque lorsque les anticipations des agents sont hétérogènes et les ventes à découvert sont restreintes. Il apparaît alors que les restrictions sur les ventes à découvert induisent un coût d'opportunité qui réduit le taux de rendement anticipé. Ce coût d'opportunité devrait être une fonction positive de la dispersion des anticipations et une fonction négative du niveau de liquidité du titre. Ces hypothèses sont vérifiées à l'aide de données mensuelles, qui couvrent la période de0101 1985 à1101 1989. La méthodologie de Litzenberger et Ramaswamy (1979), est utilisée afin de résoudre les divers problèmes économétriques. Les résultats montrent une relation linéaire négative entre le rendement des titres et le niveau d'hétérogénéité des anticipations, mesuré par la dispersion des prévisions des analystes financiers. Cette relation est surtout observable pour les titres les moins liquides, qui sont ici les moins suivis par les analystes financiers. Ces résultats valent pour chaque sous période et résistent à l'introduction de variables de contrôle.This paper examines, in a Canadian context, the effect of short sales regulation on the risk-return relationship. Drawing from Jarrow's work (1980), we derive an equilibrium risk-return relationship that accounts for both heterogeneous expectations and short sales regulation. We conclude that the required rate of return on risky assets in a world where short sales are forbidden is equal to the required rate which would prevail in a world free of short sales restrictions, minus an opportunity cost induced by short sales regulation. We show that, theoretically, this opportunity cost is positively related to the dispersion of agents' beliefs and negatively related to the security's liquidity level. We test the model over the sixty-month period from January 1985 through December 1989 and use 13079 observations (220 companies on average). We pool all the observations into a time series cross-sectional model and use Litzenberger and Ramaswamy's methodology (1979) to address three econometric problems: heteroscedasticity, cross-correlation of disturbance terms and beta measurement errors. The results permit us to establish that a negative linear relationship links expected risky asset returns and the divergence of agents' beliefs. This negative relationship is consistent with the presence of opportunity costs resulting from short sales regulation when return beliefs are heterogeneous. We find that the negative relationship between security returns and dispersion of beliefs is essentially confined to illiquid securities, that is, those monitored by a small number of analysts. Finally, these results are not modified when tested on two sub-periods nor when we introduce two control variables (size, as measured by the number of analysts monitoring the stock, and January effect)

Managerial Responses to Incentives: Control of Firm Risk, Derivative Pricing Implications, and Outside Wealth Management

We model a firm’s value process controlled by a manager maximizing expected utility from restricted shares and employee stock options. The manager also dynamically controls allocation of his outside wealth. We explore interactions between those controls as he partially hedges his exposure to firm risk. Conditioning on his optimal behavior, control of firm risk increases the expected time to exercise for his employee stock options. It also reduces the percentage gap between his certainty equivalent and the firm’s fair value for his compensation, but that gap remains substantial. Managerial control also causes traded options to exhibit an implied volatility smile

Optimal Power Investment and Pandemics: A Micro-Economic Analysis

This paper derives the optimal investment policy of an electricity producer during a pandemic. We consider three problems: (1) investing in a gas-fired plant, (2) investing in a wind plant, and (3) investing in the best of a gas plant and a wind plant. Optimal investment boundaries are characterized and valuation formulas derived. For single technology projects, a pandemic postpones wind investment, but can accelerate gas investment when the relative price of gas decreases. For choices between the two technologies, a substitution effect can reinforce the single technology effects, accelerating gas investment under certain conditions. The paper examines the impact of pandemic parameters, economic parameters and policy parameters on the investment boundaries, the values of projects and the premium for green energy

Optimal Investment under Cost Uncertainty

This paper studies the valuation of real options when the cost of investment jumps at a random time. Three valuation formulas are derived. The first expresses the value of the project in terms of a collection of knockout barrier claims. The second identifies the premium relative to a project with delayed investment right and prices its components. The last one identifies the premium/discount relative to a project with constant cost equal to the post-jump cost and prices its components. All formulas are in closed form. The behavior of optimal investment boundaries and valuation components are examined