Investing is decision making under conditions of uncertainty. Uncertainty is defined by probability distributions. The probability distribution with which people are most familiar is the normal, bell‑shaped curve.
Every financial forecast is a probability distribution. To value a financial asset is to value the cash flows or payoffs that the asset's forecast allows for. Mathematically speaking, to value a financial asset is to evaluate its probability distribution.
Black‑Scholes Options Pricing Theory assumes that a forecast for a stock's future price is a normal, bell‑shaped curve drawn on a lognormal price axis.
The Black‑Scholes value of a call option is the area of the bell‑shaped curve above the call's strike price. The Black‑Scholes value of a put option is the area of the bell‑shaped curve below the put's strike price.
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