The Pricing of Options and Corporate Liabilities

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.