Assumptions of the BSM model

Question

List the assumptions under which the Black-Scholes-Merton equation is derived.

Short answer

Lognormal stock prices, constant rates and volatility, frictionless continuous trading and no arbitrage. Specifically: the stock follows geometric Brownian motion with constant $\mu$ and $\sigma$ ; the risk-free rate is constant and the same for borrowing and lending; no dividends during the option's life; no transaction costs or taxes; securities are perfectly divisible and short selling is allowed with full use of proceeds; trading is continuous; and there are no riskless arbitrage opportunities.

Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 6.1 Option Pricing, 'Black-Scholes-Merton differential equation B', p.142; question and answer rewritten by SelfMadeQuant.com.

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