The Midas Formula: Trillion Dollar Bet (1999)

The Black-Scholes Formula, by BBC Horizon

The Black-Scholes Formula was derived by observing that an investor can precisely replicate the payoff to a call option by buying the underlying stock and financing part of the stock purchase by borrowing. To understand this, consider our example of XYZ stock. Suppose that instead of owning the call option, you purchased a share of XYZ stock itself and borrowed the $100 exercise price. At the option's expiration date, you sell the stock for $120, you pay back the $100 loan, and you are left with the $20 difference less the interest on the loan. Note that at any price above the $100 exercise price, this equivalence exists between the payoff from the call option and the payoff from the so-called "replicating portfolio." Source:
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Date Added: 12 years ago.

Documentary Description

This is the extraordinary story of a beautiful mathematical formula that changed the world, the financial markets, and indeed capitalism itself. It could do the unthinkable - it took the risk out of playing the money-markets. To its inventors it brought the Nobel Prize for economics. To those who used it, it brought great wealth. But this glittering tale would end in tragedy. The Black Scholes formula was invented 25 years ago, by three young mathematicians. They had been trying to solve a problem that had plagued economists for centuries - how to counter the randomness of market forces and the irrationality of human behaviour that made the markets dangerously turbulent. Whilst pondering this dilemma, they made a remarkable discovery. Bachelier's thesis written in 1900 The search for a way to price option contracts began in earnest when the thesis of an unknown student named Louis Bachelier was unearthed in the 1950s. Working at the beginning of this century, Bachelier had set out to do something no-one had ever done before - using a series of equations he created the first complete mathematical model of the markets. He had realised that stock prices moved at random and that it was impossible to make exact predictions about them, but Bachelier said he had also found a solution - through the pricing of a financial contract called an option. Stock prices The risk in the stock market is that if you buy a stock today the price can drop in the future and you could lose money but if you pay for an option contract this gives you the right to wait and buy the stock if it reaches some agreed price in the future, but there's no obligation. If the stock fails to reach that price you can opt out and you would lose only the cost of the option. In theory options are a perfect way to get rid of risk, but there was a problem. How much would someone pay for such absolute peace of mind? Bachelier believed that if someone could discover a formula that would allow option contracts to be widely used, they would be able to tame the markets completely, but he died before he could find it. By the end of the 60s, academics were no nearer to pricing options than they'd ever been. But all this was about to change when Myron Scholes and his colleague Fischer Black set out to tackle the problem of options…

At its simplest level, the Black Scholes formula could be used to hedge against losing any bet, by working out how to place another bet in the opposite direction. That way, you couldn't lose. The formula had the almost magical ability to allow you to make a fortune with the minimum of risk. But there was one problem. In the time it took to make the calculation, the fast moving markets had moved on and the calculation would effectively be out-of-date. However, unbeknown to them, the problem had already been solved by a financial genius called Bob Merton. Using an idea taken from rocket science, the value of an option could now be constantly recalculated and the risk eliminated continually. Traders Myron Scholes and Bob Merton joined forces with the greatest dealers on Wall Street, and started a legendary company - Long Term Capital Management (LTCM). Relying on mathematics, the company traded and borrowed on a scale never seen before. But the mathematical model was based on normal market behaviour and unforeseen events were about to send the markets wild. The calculations in LTCM's models became hopelessly out of kilter, and when the company collapsed last year, it nearly brought down the entire global economy.
Source: BBC

Resources from PBS/NOVA:
The film tells the fascinating story of the invention of the Black-Scholes Formula, a mathematical Holy Grail that forever altered the world of finance and earned its creators the 1997 Nobel Prize in Economics. Here's what you'll find online:

  • The Formula That Shook the World
    One economist has likened the impact of the discovery of the Black-Scholes Formula to that of the discovery of the structure of DNA. Delve into the inner workings of the formula - if you dare.
  • Impact of Online Trading
    Seems like everybody is getting into the game of trading stocks over the Internet. Here, a columnist for The, an online investment and financial news publication, takes a sidelong glance at this exploding phenomenon.
  • A Trader's Lexicon
    You probably know the difference between a bull and a bear market. But what about the difference between a call and a put? A trend line and a trend break? Whisper numbers and whipsaws? Get the answers in our online glossary.
  • Play a Virtual Market (Hot Science)
    Want to play the stock market without risk? Here we give you a virtual fortune and several leading stocks to spend it on. Caution: These stocks may be volatile.


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