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CBOE Holdings, Inc (CBOE): The Secrets Of The Black-Scholes Formula

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CBOE Holdings, Inc (NASDAQ:CBOE)On this day in economic and business history…

The Black-Scholes option-pricing model, first published in 1973 in a paper titled “The Pricing of Options and Corporate Liabilities,” was delivered in complete form for publication to The Journal of Political Economy on May 9, 1972. PBS’ NOVA offers the following explanation of the model, and of its importance to the financial world:

Derived by economists Myron Scholes, Robert Merton, and the late Fischer Black, the Black-Scholes formula is a way to determine how much a call option is worth at any given time. The economist Zvi Bodie likens the impact of its discovery, which earned Scholes and Merton the 1997 Nobel Prize in Economics, to that of the discovery of the structure of DNA. Both gave birth to new fields of immense practical importance: genetic engineering on the one hand and, on the other, financial engineering. The latter relies on risk-management strategies, such as the use of the Black-Scholes formula, to reduce our vulnerability to the financial insecurity generated by a rapidly changing global economy.

Here’s the theory behind the formula: When a call option on a stock expires, its value is either zero (if the stock price is less than the exercise price) or the difference between the stock price and the exercise price of the option. For example, say you buy a call option on XYZ stock with an exercise price of $100. If at the option’s expiration date the price of XYZ stock is less than $100, the option is worthless. If, however, the stock price is greater than $100 — say $120, then the call option is worth $20. The higher the stock price, the more the option is worth. The difference between the stock price and the exercise price is the “payoff” to the call option.

The Black-Scholes model helped legitimize the CBOE Holdings, Inc (NASDAQ:CBOE), which began trading in 1973, around the time that Black and Scholes’ paper was first published. In 2012, the CBOE Holdings, Inc (NASDAQ:CBOE) transacted over 575 million call options and 535 million put options, which implied a total dollar volume worth $575 billion.

However, this is only a small slice of the total value of financial derivatives traded around the world. Deutsche Borse estimates that the worldwide derivatives market has grown at an annualized rate of 24% per year for the past quarter-century, but this, too, may understate the staggering scope of the worldwide derivatives market. Prior to the financial crisis, the notional value of this market reached an estimated $600 trillion. Five years after the crash ended, some new estimates place the total value of global derivatives at $1 quadrillion. For a sense of the sheer size of that much money were it ever made manifest, picture a tower of $100 bills, about two-thirds of a mile high. That’s $1 billion. A quadrillion dollars in stacked $100 bills would be nearly three times as tall as the distance from the Earth to the moon. In slightly more earth-bound terms, $1 quadrillion is 15 times the size of the entire world’s annual gross domestic product. Under this simplistic measure, it’s hard not to call the Black-Scholes model the most valuable mathematical model ever created.

Holding back the banks
President Dwight Eisenhower signed the Bank Holding Company Act, or BHCA, into law on May 9, 1956. This is a complex law that has undergone various policy shifts and legislative modifications over time in response to the changing conditions of the financial industry, but it continues to act as a foundational piece of financial-industry regulation to this day.

The Eisenhower era, though somewhat more conservative than the New Deal era it supplanted, retained a fundamental distrust of high finance that had colored national perceptions since the Great Depression. It was in this spirit that the BHCA became law. The BHCA effectively barred bank holding companies from expanding across state lines, and also restricted these institutions from engaging in most non-banking activities. Prior to this, the holding company structure would have allowed banks to evade most geographical or commercial restrictions in a rather blatantly transparent way.

Although the scope of acceptable banking activities was gradually expanded over time, it was not until the Rigele-Neale Act of 1994 that interstate banking restrictions were fully lifted. The Gramm-Leach-Bliley Act of 1999 removed many restrictions on allowable banking activities, leading to a wave of industry consolidation that had already begun with the technically illegal-at-the-time 1998 Citigroup merger. The BHCA remained in force as a barrier between banking and pure commerce.

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