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Have you solved it yet? For example in the drift parameter, the dt needs to be vector of time from 0 to 1 by dt. My code is: GBM<-apply(BM,2,function(x) 100*exp((cumsum((r-0.5*sigma*sigma)*time)+sigma*x))) where I'm using GBM on already cumsummed Brownian Motion (x).

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Seems like you are running cumsum on a normalised vector - which'll give you zero as the end value for each path. Also, in the GBM, the drift term (-sigma^2*dT) needs to accumulate over time.

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The assumption of 100% delta for an option would give a good upper estimate for the exposure due only to the part of the option exposure that comes from the movements in the underlying price. But for example, imagine you had a portfolio which is long a long dated call and long a long dated put, such that the portfolio is overall delta neutral over a ...

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