# 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: http://www.pbs.org/wgbh/nova/stockmarket/formula.html
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### Documentary Description

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the time it took to make the calculation, the fast moving markets had moved on and the calculation would effectively be out-of-date.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.