More thoughts on the Black-Scholes Quandary

I appreciated the comment from Sebastien Bossuposted to a May 1 blog I did for the CBOE community about Black-Scholes. Here are my responses:

My primary issue concerning the assumed “risk-free” interest rate is not which rate to use, but my observation that no such thing exists. At the time B-S was published (and ever since) this has most often been a reference to U.S. Government bonds. But now that the U.S. credit rating has been downgraded, I am no longer sure the world financial community sees U.S. debt as risk-free. Perhaps a corporate bond of an exceptionally strongly capitalized corporation — and its interest rate — would present a more realistic version of this hypothetical rate.

It is true that modifications to the B-S formula may allow for American-style exercise and dividends. Even so, the calculation remains questionable for one additional and profoundly serious flaw: The formula assumes that implied volatility determined at the time of calculation remains unchanged until expiration. We all know that this never happens, again making the formulation theoretical but hardly practical.

The B-S formula might indeed represent the cost of replication at a fixed moment in time, but it provides little actionable information about an option’s market value. The responder’s analogy to a fruit salad is right on the money. You can mix apples and oranges to make a fruit salad, and you can mix stock and cash to manufacture an option (or its assumed value). Although B-S is put forth as a solution to figuring out a fair price, I remain convinced that B-S does not accomplish the claimed solution. Many investment managers or individuals might use B-S as modeling devices (although I have not yet met one who does so reliably), but I think the pricing model ends up being much less useful than the hedging properties of some strategies, coupled with IV timing, probability, and awareness of profit and loss zones.

If you can time your entry and exit based on these, why do you even need a price model? The usual method traders use is a profit model, not a pricing model.

Michael C. Thomsett

About this week’s Heavy Hitter: Michael C. Thomsett is a widely published options author, with six options books in print, published by John Wiley & Sons, FT Press, Amacom Books, and Traders Library. He has recently signed a contract with Palgrave Macmillan for a two-book deal, both books on options topics.