I liked our present method of valuing options pretty well right up until the moment when it was finally time to put some of my own hard-earned money at risk by selling one. I could still understand the logic of the mathematical argument, but somehow the idea of selling an uncovered call, or even an incompletely covered call, myself, just seemed crazy to me. There are ideas we can advocate in public without looking foolish, and then there are ideas we would really act on in private, even if nobody else could see what we were doing. Somehow it suddenly seemed to me, then, that Black-Scholes, like so much of the rest of modern finance theory, actually belonged in the first category but not the second.
What I want to talk about here is what I would really do instead of just using Black-Scholes in its present form, and why. The question that interests me is a practical one about how you or I, as prudent people, ought to actually account for the actual options that we might actually buy or sell some day soon. I’m going to confess to you how I, personally, would do things, and try to rationally justify my own choices, which I admit is not as good as giving you a scientific theory that spits out a precise numerical value as the absolute, eternal, observer-independent, peer-reviewed truth. But, after all, my subject is a mere accounting rule, and Aristotle tells us that we ought to treat each subject with the degree of precision it deserves, so perhaps there’s even something principled about my refusal to claim to be doing hard, objective science.
What is it, intuitively, that seems so wrong about Black-Scholes? Any reasonably cautious person who sees the way options are promoted to small investors on CNBC can’t help but be bothered by the fact that our present theory of option valuation presents the risks of buying options and the risks associated with selling them as being exactly the same, even though one activity involves only a limited possible loss, while the potential losses from the other are unlimited.
Continue reading "How Options Should Be Valued" by Daniel Cloud, Ph.D. 