The stop-loss start-gain paradox and option valuation: A new decomposition into intrinsic and time value

The downside risk in a leveraged stock position can be eliminated by using stop-loss orders. The upside potential ofsucb a position can be captured using contingent buy orders. The terminal payoff to tbis stop-loss start-gain strategy is identical to that of a call option, but tbe strategy costs less initially. This article resolves tbis paradox by sbowing tbat tbe strategy is not self-financingfor continuous stock-price processes of unbounded variation. The resolution Of the paradox leads to a new decomposition of an option's price into its intrinsic and time value. When the stock price follows geometric Brownian motion, this decomposition is proven to be matbematically equivalent to the Black-Scboles (1973) formula.