Not even Samuelson himself believed that the 1965 paper was correct. See below.
Samuelson, P., Merton, R.C.; "A Complete Model of Warrant Pricing that Maximizes Utility", Industrial Management Review, MIT, 1969, page 31
"Admittedly, out new theory has arrived at the same paradoxical result as the special case of the 1965 theory [Samuelson paper referenced in the NBER paper by Lerner], namely that a perpetual warrant should sell for as much as the common stock itself. Such a result would seem empirically bizarre. In real life, perpetual warrants generally do sell for less, and since the common stock is equivalent to a perpetual right to itself at zero exercise price, one would have thought it would dominate a perpetual warrant exercisible (sic) at $1. Indeed, one of the purposes of the general 1965 theory was to construct a model that would keep perpetual warrants down to a price below the common [stock].
What is there to do about the paradox? First, one can recognize that the common stock maybe paying dividends now or can be expected to pay dividends at some time in the future...Finally, we can dispel the paradox by accepting it as prosaic...Hence, why should not the perpetual warrant sell for essentially the same price as the common? And, if people believe this will be the case, it will be a self-fulfilling belief."
Now, the difference between a $1 strike and a $0 strike (the stock itself) may be minimal if the stock is selling for $25, but you cannot reach the same conclusion if you are talking about the difference between a $100 strike and a $0 strike, especially if the stock is selling for $25. |
