We analyze the effects of optimism and overconfidence when the manager's compensation package includes severance pay and the CEO has some bargaining power. We find that overconfidence reduces incentive pay as found by previous literature but (when high enough) increases severance pay, while managerial optimism increases severance pay with no countervailing effect. For high values of overconfidence the incentive compatibility constraint cannot be satisfied and an inefficient level of investment is chosen. Our simple model helps explaining several features of the large severance payments documented by empirical literature. It shows that the optimal contractual severance pay is lower than the actual payment in case of turnover; and that the overall severance payment to the departing CEO is larger than the incentive pay in case of success. Consequently, the attempt to exploit the lower cost of incentives due to overconfidence, may backfire if the CEO is replaced.