The Valuation of Market-Leveraged Stock Units

Abstract

It has become very popular to compensate executives partly with options on the firm’s stock. The exposure to the future performance of the stock provides an incentive for the manager to do his best to increase firm value. But this incentive can become greatly diminished if the stock price falls below the option’s strike, while grants of restricted stock do preserve performance incentives over all future stock prices. A variant on restricted stock, the market-leveraged stock unit (MSU), is beginning to be seen. At maturity, this contract pays the holder a minimum number of shares if the stock price is below a lower bound, a maximum number of shares if the price exceeds a set upper bound, and a variable number of shares equal to the ratio of the final price over the initial price if the final stock price is in between the two bounds. Hull and White provide valuation formulas for plain-vanilla MSUs as well asfor a generalized form of the contract.