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Apart from the usual risks measured by Greeks there's risk associated with volatility dynamics. Volatility surface moves with stock movement and is usually dependant on stock price level. This risk is usually modelled by extensions to volatility models that take underlying price into account or stochastic volatility models (e.g. SABR). The way to do ...

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This is perhaps not a concrete solution to your problem but the space in the comments is limited :) In your setupt you are not actually pricing an option on a basket but on a dynamically allocated portfolio. Thus conventional pricing and hedging approaches won't apply. Also you are underestimating porfolio optimization algarithms. To find an optimal ...

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I would define the weights $w_1,\ldots,w_n$ as whatever number you want and the basket given by $$B_t = \sum_{i=1}^n \frac{w_i}{W}S_t^{(i)}\ , \qquad W = \sum_{i=1}^nw_i$$ so the weights always sum to one. This doesn't make much sense, however, because you are changing the product, not a market variable. This meaning that when the weights change, the ...

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