Black-Scholes Option Pricing
No-arbitrage pricing of options, the formula that built modern derivatives markets.
Definition
The no-arbitragearbitrageRiskless profit from price differences, whose pursuit eliminates those very differences. option-pricing model: continuously hedging a stock-plus-borrowing portfolio replicates the option, so its price follows from volatility, not expected returns.
Key equation
C = S·N(d₁) − K·e^{−rT}·N(d₂)
The intuition
The stock's expected return doesn't appear in the formula, the deepest result in finance: hedging removes direction risk, leaving only volatility to price. Traders quote implied volatility precisely because the formula inverts cleanly.
Exam tip
Know the drivers' signs: option value rises with volatility and time (for calls, with S and r; falls with K).
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