The Fallacy of Fully Dividend-Protected Stock Options and Convertible Bonds

Abstract

Altering the terms of a call option to fully protect its value when the underlying stock goes ex-dividend turns out to be trickier than one might think, and the same problem applies to protecting a convertible bond when a stock dividend is paid. Simply lowering the strike price by the same proportion that the stock price falls reduces (S – X) by the same percentage, so to maintain the option's intrinsic value in dollars, the number of options must also be increased. This re-striking method equalizes the option's exercise value before and after the dividend, but the volatility of the underlying still changes. Zimmermann proposes a new correction method that preserves option value when dividends are paid. The difference between valuation under the new method and under the re-striking method is not insignificant, amounting to several points of implied volatility for a holding period of three to five years.