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Black Scholes — Is There An Alternative?

The drawbacks of the Black Scholes pricing model are well-known and, while used in a limited way by some, the majority of trades find no value in the pricing model.

But there are other ways to calculate and model price.

First of all, what is the reason for pricing models? You want to know what, in theory, the option "should" be worth so you can better judge current premium as high or low. (In other words, maybe you really only need to track implied volatility of a specific option to decide this.) But beyond the basic need to know how to judge current premium, is there a better method?

The "risk-free interest rate" used by the B-S model is a huge problem. Can anyone explain what this is? In our modern debt security environment, what is a risk-free rate? B-S also assumes European style and no dividend, clearly not applicable to the majority of equity options traded today.

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. Or, for dividend-yielding stocks, the dividend yield may also serve this purpose.

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. 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.

A logical pricing model should be based on the fundamentals of the underlying security rather than on some universal "assumed" variables like risk-free rates. Because options are tied specifically to the underlying security, why should we use a broad assumption? For example, there may be a more reliable model of "return" based on return to investors mingled with the price of the underlying. The PE/book, for example, combines these elements. You have all of the elements: price of the stock, EPS, and tangible book value. This boiled-down return is perhaps much more suitable as a means for pricing options than the outdated B-S model.

It comes down to a question of what is reasonable and realistic. In trading options over 46 years, I have never met a trader who makes timing decisions based on the B-S model.

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