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Thorp, Black, Scholes, and Merton

Finance started to diverge from statistics in the decade around 1970. We could start with Ed Thorp's first development and use of an option pricing model in the 1960s, or the publication of Fischer Black's and Myron Scholes's famous 1973 paper, “The Pricing of Options and Corporate Liabilities,” or the publication of Robert Merton's paper, “Theory of Rational Option Pricing,” the same year.

Popular finance books usually describe the Black-Scholes option pricing model as horrendously complex and requiring advanced mathematics. That's silly. The basic idea is simple. Some of the technical details in proving it are complicated, and the formula itself looks a bit intimidating compared to, say, 2 + 2 = 4, but that's no reason to ignore the insight.

Suppose there is a stock that sells for \$70 today and will be worth either \$100 or \$50 tomorrow. What is an option to buy 100 shares of the stock at \$80 per share tomorrow worth? Your first thought might be zero. You can buy the stock for \$70; why would you pay for the right to buy it at \$80? The reason the option has value is you get to choose whether to buy tomorrow, after you know the new stock price. The option is worth \$2,000 (\$20 per share) if the stock goes up, and zero if the stock goes down.

Suppose you bought 40 shares of stock. These will be worth \$4,000 tomorrow if the stock price goes up, and \$2,000 if the stock price goes down. Either way, they're worth \$2,000 more than the option. Since 40 ...

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