Black-Scholes model: a standalone construct

Fischer Black and Myron Scholes, in their 1973 paper The pricing of options and corporate liabilities, derived a closed-form formula for the fair price of a European option, a contract giving the right to buy or sell an asset at a fixed price on a single fixed future date, from the underlying asset's current price, the option's strike price, the time remaining, the risk-free interest rate, and the asset's volatility, meaning how much its price fluctuates. Their argument rests on no arbitrage: by continuously trading the underlying asset against the option a trader can build a position with no risk, and requiring that this hedged position earn only the risk-free rate yields a partial differential equation whose solution is the pricing formula. That same year Robert Merton, in Theory of rational option pricing, restated and generalised the result on firmer mathematical footing and extended it to assets that pay dividends, and the joint contribution is often called the Black-Scholes-Merton model. The model is a landmark because it gave options, once priced by rule of thumb, a single derivation resting on observable inputs, with volatility the one input not directly observed, and it underpins much of modern derivatives trading and the field of financial engineering.[1][2]

Unit

A pricing model: a formula and the partial differential equation behind it that return the fair value of an option

Recovery means

Not applicable

Measured by

Applied by supplying the underlying price, strike, time to expiry, risk-free rate, and volatility; volatility is estimated from historical returns or inferred from market prices as implied volatility