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Correlations between what? Correlations between stock A and another stock B - relative value arbitrage - not sure if small correlations will help here. Correlations between stock A and its future stock return Ra - its called Information Coefficient. Try Fundamental Law of Active Management and many similar web info on Fundamental Law for more information. ...


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You're making it much more complicated than it has to be. Remember that the arbitrage free price is given by $e^{-r(T-t)}\mathbb{E}(\Phi(S_T))$ (to be correct, this should be conditioned on the appropriate sigma-algebra. I'll exclude that for ease of writing). Now use Itos on $\ln(S_t) = X_t$, this yields, after integration (Note that you integrate from $t$ ...


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it is based on Kelly criterion. mentioned in one of stackexchange posts here .


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you never trade spot volatility. you exchange it for something else. if you want to exchange it for spot implied volatility, you buy a volatility swap. if you want to exchange it for forward implied volatility you get options.


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As I see it the question does not enforce that the market is free of arbitrage. This is why you can get to contradicting prices. Thus you can't actually apply a risk-neutral argument here without making additional assumptions. You yourself provide the example of such an arbitrage. If the underlying process had a B&S dynamics you could just borrow money ...



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