Black-Scholes/Merton is wrong

The theory developed by Fischer Black, Myron Scholes, and Robert C. Merton III is wrong. Not just a little bit wrong, but wrong in a way no Nobel Prize can redeem. Merton provided a closed-form solution for barrier options using the reflection principle of Brownian motion. What is the value of a barrier option that knocks in the second time the barrier is hit? It is the same as a barrier option that knocks in the millionth time it is hit. Don’t be like me and actually say that to a trader. Charlie didn’t speak to me for 3 months after I made that mathematically correct, but totally foolish claim. I managed to redeem myself by helping him with some statistics he needed for his Fantasy Football hobby.

This ridiculouness is a mathematical artifact of Merton learning the Ito calculus at Cal Tech. It leads to the untenable notion of continuous time trading. I have been guilty of teaching this nonsence to unsuspecting students at NYU, Cornell, Rutgers, and Columbia in the derivative securities I’ve taught. The way it works in the real world is traders do only a finite number of trades.

It is time to put an end to this.