Ian Stewart and the Black-Scholes equation

The Black-Scholes equation is an economical tool used in financial contracts. Following Ian Stewart (via Alexandre Borovik), this equation caused the economic crash and crisis. We can immediatly say that we must not use mathematics to describe the financial system, but the problem isn't in the equation, is in his use:
The formula was fine if you used it sensibly and abandoned it when market conditions weren't appropriate. The trouble was its potential for abuse. It allowed derivatives to become commodities that could be traded in their own right. The financial sector called it the Midas Formula and saw it as a recipe for making everything turn to gold. But the markets forgot how the story of King Midas ended.
The equation was derived by Black and Scholes in 1973, in the paper The Pricing of Options and Corporate Liabilities. In the same year Robert Merton in the paper Theory of Rational Option Pricing develop the mathematics under the equation and the options, starting from the model of Fischer Black and Myron Scholes. For their work Scholes and Morton won the Noble Prize in economics in 1997 (Black died in 1995).
Now, one of the background ideas in Black and Scholes original model is the brownian motion, a mathematical model used to describe the random motion of a particle in a fluid. So it could be right use a brownian model in the study of the financial networks, but is also a great simplification of the problem:
Large fluctuations in the stock market are far more common than Brownian motion predicts.
So we need a more complex model in order to describe the financial word, as Stewarts writes:
The Black-Scholes equation has its roots in mathematical physics, where quantities are infinitely divisible, time flows continuously and variables change smoothly. Such models may not be appropriate to the world of finance. Traditional mathematical economics doesn't always match reality, either, and when it fails, it fails badly. Physicists, mathematicians and economists are therefore looking for better models.
Stewart suggests to use the tools of complexity science, that are just used in econophysics, a collection of mathematical tools developed by some physicists strating from the equation of Gell-Mann and Shannon in complexity and information theory. Econophysics is not so accepted by theoretical economists (the mainstream economists), but it
is having some impact on the more applied field of quantitative finance, whose scope and aims significantly differ from those of economic theory. Various econophysicists have introduced models for price fluctuations in financial markets or original points of view on established models. Also several scaling laws have been found in various economic data.
The approach of econophysics (and the approach of science) is simple: first of all we try to describe the past, and after we try to predicts the develop of the financial network. So I think that, in order to describe financial network, we need of more complex model based on network theory and physics equations, and simulation with more and more variables than Black and Scholes equation. So we could conclude that this equation blames for the finantial crash. The solution is not so simple (but is clear now):
Black-Scholes may have contributed to the crash, but only because it was abused. In any case, the equation was just one ingredient in a rich stew of financial irresponsibility, political ineptitude, perverse incentives and lax regulation.
The world economy desperately needs a radical overhaul and that requires more mathematics, not less. It may be rocket science, but magic it's not.

1 comment:

  1. Dear Mr Filippelli,

    I've just read your article which ideas I completely share and support.
    With this I want to inform you and Mr. Stewart that the new mathematics solving some of the problems mentioned in the article one can find in my papers:
    Management Studies (2020), 8(3), 191-214,
    ACRN-JOFRP, (2020), 9, 148-176; http://www.acrn-journals.eu/resources/jofrp09l.pdf
    Management Studies (2020), 8(6), 430-452,

    The main message of these papers is that financial economics in its present form is now completing the period of its development which founded on the works of Kendall (53), Onsager (59), Modigliani & Miller (58-63), Black & Scholes (73), Merton (74), Harrison (80), Leland (94), and their multiple followers. I have shown that Modigliani-Miller Propositions, Merton's real options, the risk-neutral probabilities, and the no-arbitrage pricing principle are generally wrong. Their deficiencies follow from the use of the oversimplified Geometric Brownian model (GBM) introduced by Black & Scholes and ignoring the firm's compulsory payments, such as fixed costs, debt payments, taxes, and dividends. Detailed criticism of the traditional theories one can find in my papers. No attempt rejecting my approach and defending the traditional theories by proving their soundness mathematically has been made so far.
    Could you please resend this message to Ian Stewart for more professional discussion?

    Sincerely yours,
    Valery Shemetov


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