How Are Options Priced? Black-Scholes and Binomial Models
Options give the right (not obligation) to buy or sell at a set price. Black-Scholes gives us the mathematically precise fair value of this right.
FV, r, n) โ or type numbers directly: 10000 / (1 + 0.08)^1010000 / (1 + 0.08)^10An option is the right to buy (call) or sell (put) something at a fixed price in the future. The question: how much should this right cost today? Black-Scholes gives a mathematical answer based on price, strike, time, interest rate, and volatility.
Black-Scholes: Call value = S ร N(d1) โ K ร e^(โrT) ร N(d2). N(d1) is the probability of exercise (roughly). Higher stock price, lower strike, more time, and higher volatility all increase call value. The key insight: higher volatility is GOOD for option holders โ more chance of big upside while downside is capped at $0.