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[Applause] [Applause] hi everyone we all know the black shull formula is one of the simplest things but the symbols can conceal the simplicity so letamp;#39;s try to uncover the simple idea behind the formula we all been told that it assumes the stock price follows geometric brownian motion actually thereamp;#39;s a drift element to it and a good story around why the market will force the drift rate to be equal to the bank rate which you might know is the risk-free rate but it wonamp;#39;t make much of a difference to the explanation here so letamp;#39;s assume we are in a zero interest rate environment this assumption doesnamp;#39;t sound as unrealistic today as it used to a decade ago for european options the gbm assumptions really amounts to saying that the stock price at a future date is log normally distributed with mean equal to log of s naught minus half the variance and standard deviation equal to sigma times square root of t this is of course an as
