by R. Passov

Modeling in finance is done through the lens of mathematics. To put something into a model where you are not guided by observable constants, such as the speed of light, requires assumptions.
With so many models off the shelf a common understanding of assumptions is slipping by. If you go far enough back, most good finance text books bothered to explain the assumptions underlying the model. One such text – Modern Finance by Copeland and Weston – offers a comprehensive discussion of the assumptions necessary to argue that the world of asset pricing is mean-variant efficient (MVE.)
MVE underpins the Capital Asset Pricing Model (CAPM), the second most important model in all of finance; a model most students in business classes in western universities are exposed to; and something that simply can’t work. Much can be proven about what the model can say.
The most important of which is that there’s a certain portfolio of assets – the Efficient Frontier – that is better than all others.
But it turns out that while this portfolio can always be found in historical data, it can never be identified in the present.
But there are other models which can be derived from the same set of unrealistic assumptions. In 1997, The Nobel Prize committee awarded the prize in Economic Sciences to Robert Merton and Myron Scholes for their “… method to determine the value of derivatives,” – the Black Scholes Options Pricing Model (BS).
These two, along with Fisher Black who had passed prior to the award, solved the puzzle of pricing the right which affords its holder a specific time frame within which to purchase, for a set price, a risky asset. The right can be to buy (a call) or sell (a put) or otherwise manipulated in almost any fashion that mathematics allows, and still some form of the BS equation will arrive at a price.
The assumptions necessary for the options pricing model to mirror reality have never been met. And yet, pricing options and the reams of creative derivatives that spew forth is a several-hundred-trillion-dollar market.
The notional value of derivatives collapse, or ‘net,’ to a much smaller number as most activity is part of a giant zero-sum game. Still, options exist. Farmers have long since contracted in advance to sell yet-to-be harvested crop. It’s only in the past 45 years that a workable formula has been available to help someone negotiate a price.
The basic formula was derived in 1900 by a French mathematician. Read more »