The Pricing of Options and Corporate Liabilities
Price an option not by guessing the stock's direction, but by hedging the risk away.
How much should you pay today for the right — but not the obligation — to buy a share at a fixed price next year? In 1973, two economists turned that question into a formula.
The big idea
An option is a contract that gives you the right to buy a stock at an agreed “strike” price on some future date, without forcing you to. If the stock soars, you buy cheap and pocket the difference; if it sinks, you simply walk away. That one-sided bet is obviously worth something — but how much? Fischer Black and Myron Scholes found the answer through a trick: they showed that an option can be exactly mimicked by holding a carefully chosen, constantly adjusted mix of the stock and cash. If you can build a copy of the option out of things whose prices you already know, then the option must cost the same as the copy — otherwise someone could earn free money buying one and selling the other. That single insight pins the price down.
The surprise inside the formula is what it ignores. The fair price does not depend on whether you believe the stock will rise or fall. It depends on today's price, the strike, the time remaining, interest rates, and above all on volatility — how much the stock jumps around. A wilder stock makes the option more valuable, because the right-without-obligation lets you keep the big upswings while ducking the big falls.
How it came about
Black was a physicist turned finance theorist; Scholes a young economist. They had circled the option problem for years, and the breakthrough was the hedge — the realisation that pairing an option with just the right amount of stock cancels the risk. Robert Merton, working in parallel, rebuilt the argument with heavier mathematics and gave the model its name. Their paper was rejected by two journals before the University of Chicago's Merton Miller and Eugene Fama insisted it deserved a serious hearing; it appeared in 1973 — the same spring the Chicago Board Options Exchange opened its doors.
The timing was uncanny: a brand-new marketplace suddenly had a formula to price exactly what it traded, and within a year traders were punching it into handheld calculators. In 1997 Scholes and Merton received the Nobel Prize in economics. Fischer Black had died two years earlier, and the prize is not given posthumously — so he was named in the award but could not share it.
Why it mattered
Before 1973, pricing an option was largely guesswork. Afterwards there was a shared, defensible number — and a recipe for cancelling risk by hedging. That gave banks the confidence to create and trade derivatives on an enormous scale, and built much of the modern financial industry. But the same formula carried a quiet warning the world relearned the hard way: in the 1998 failure of a fund run partly by Scholes and Merton, and again in the 2008 crisis. A hedge that is perfect on paper assumes you can always trade smoothly — and when markets freeze, that assumption fails.
A way to picture it
Think of insurance. An option is a lot like a policy that pays out only when a price moves your way. How does an insurer set a premium? Not by betting on whether your particular house will burn down, but by knowing how likely and how large the possible losses are, and by spreading the risk across a balanced book. Black and Scholes did the same for options: they priced the bet not from a hunch about direction, but from the size of the swings — the volatility — and from the ability to keep rebalancing a hedge, the way an insurer holds a balanced book of policies.
Where it sits
The idea that prices wander randomly goes back to Louis Bachelier in 1900, who described stock movements with the same Brownian-motion mathematics Einstein would later use for atoms. Black–Scholes turned that picture into a usable price, and in doing so created quantitative finance — a field that sits between the economics of Smith, Ricardo and Keynes elsewhere in this Library and the probability of Bayes. From here the line runs to the VIX “fear index” quoted on the news, and to the vast — and sometimes dangerous — world of derivatives.
If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
It is possible to create a hedged position, consisting of a long position in the stock and a short position in the option, whose value will not depend on the price of the stock.