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I think that the question in its current form is not really precise. The Greeks are quite easy to define for a given formula of a price: in that case they are simply partial derivatives, and of course linear (and in some case commute with integrals rather than just finite sums). However, they are crucially model-dependent - not only their expressions, but ...


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Well if we take a call option the gamma is non-zero. If we take the replicating portfolio for a call option, it consists of stock and bonds. Both of these have zero gamma. So in the form asked, I think the result is false for second derivatives.


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Yes, and as the FX market is suposed to never close, it can fluctuate 24/7, which makes it dangerous if you are not really aware of your exposure.


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Well, thats not an easy task. Because you can't predict the movement of the market. But if you want to do it based in historical data, you only have to apply the Modern Portfolio Theory by applying a Markowitz Model, which maximices the Sharpe Ratio. I have done it with Excel, is not hard but you need to know the steps, there are many tutorials, just ...



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