Name the assumptions behind the Black–Scholes–Merton model for valuing options
The idea
In Black–Scholes–Merton the underlying follows geometric Brownian motion, so prices are lognormally distributed and continuously compounded returns are normal. Volatility and the risk-free rate are known and constant, trading is continuous and frictionless, short selling is allowed with full use of proceeds, there are no arbitrage opportunities, and the options are European. Income such as dividends or a foreign interest rate enters as a known continuous yield. Because prices are lognormal, they cannot become negative. The model does still price an American call on a non-dividend-paying share, since early exercise is never optimal for it while interest rates are not negative. The trap is saying prices, rather than returns, are normally distributed, or that volatility may vary over time within the model.
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