The Black-Scholes Random Walk Assumption. Consider a stock whose price is SIn a short period of time of length dt the change in the stock price is assumed to be normal with mean mSdt and standard deviationm is expected return and s is volatility. The Lognormal Property. These assumptions imply ln ST is normally distributed with mean:and standard deviation: Because the logarithm of ST is normal, ST is lognormally distributed.
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