The Pricing of Options and Corporate Liabilities
Fischer Black, Myron Scholes · 1973
"An option can be priced by constructing a continuously rebalanced hedge, yielding a closed-form value independent of the investor's risk preferences."
An option is a contract giving you the right (not the obligation) to buy or sell a stock at a fixed price later. The hard problem was always: what should that right cost today? Black and Scholes showed that if you continuously buy and sell just the right amount of the underlying stock alongside the option, you can build a combined position that has zero risk — it earns exactly the risk-free interest rate no matter what the stock does. Because that riskless combination has a knowable value, you can work backward and solve for what the option itself must be worth, using only five measurable inputs: the stock price, the strike price, time remaining, the risk-free rate, and the stock's volatility.
The mechanism is arbitrage-based hedging, not forecasting. The insight isn't 'predict where the stock will go' — it's 'construct a portfolio (long the stock, short the option, in a precise ratio that changes continuously) whose value doesn't depend on where the stock goes at all.' Because that hedged portfolio is riskless, basic market logic (no free lunches) forces its return to equal the risk-free rate — otherwise arbitrageurs would exploit the gap until it closed. Solving that equation backward gives a single, closed-form price for the option that doesn't require knowing the stock's expected future return or the investor's personal risk tolerance — only its volatility. That's what made it usable at industrial scale: two counterparties with wildly different views on where a stock is headed can still agree on the option's fair price.
Why doesn't the Black-Scholes formula require knowing an investor's risk tolerance or the stock's expected future return?
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The explanation above is written with AI assistance. These are the originals — go to them to check it.
- The Pricing of Options and Corporate Liabilities (original paper)Journal of Political Economy, 1973
- In Our Time: The Black-Scholes FormulaBBC Radio 4
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