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1

Number one, the central limit theorem means a lot of things that may not be normal end up looking normal when lots of little 'experiments' or impacts are added up. Number 2, when dealing with finance you need a model that seems plausible. An arithmetic Brownian motion could go negative, but stock prices can't. On the other hand, it seems quite plausible ...


3

Your characterisation is correct but incomplete. 1) The most important part of Black-Scholes is not the model but the more general framework of dynamic hedging: you can replicate your payoff by continuously trading the underlying and the amount (delta) you should hold is the derivative of the current premium with respect to the current spot. This is a much ...


2

Might not be the answer you're looking for, but just some thoughts that immediately come to mind... As you've alluded to, the BS model is much more than just a tool to price options. But there's no need to get into this here. Prior to publication of the BS model, option prices already traded at more-or-less the price implied by B.S. (part of the ...


1

If someone wants simple intuition, here is what happened to the drift. It did go into the formula, believe it or not, but it came into the B-S math sort of in two ways so it cancelled out in the end. It disappears because Black-Scholes assumes people may have different preferences for risk, but at least everyone is consistent on their own preference. ...


0

I think you are answering your own question. Hull states: "When $\Theta$ is large and positive, $\Gamma$ tends to be large and negative and vice versa." In practice, you can expect $r(V-S \Delta)$ to be quite small.


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The error is in the application of Girsanov theorem. We have multivariate Black-Sholes market, however I apply one-dimensional Girsanov theorem. I should apply multi-dimensional Girsanov theorem. Then there would be now such equations, except the case for $\rho=1$. The alike task is formulated here ...



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