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You want to work directly with $\overline{X}$, and not some other r.v. with the same distribution, since equivalence in distribution doesn't imply that correlation remains the same. For ease of notation, I'll assume that $\mu = 0$ and $\sigma = 1$. I claim that $$ \text{cov}\left(\overline{X},X \right) = \frac{1}{t} \int_0^t s \ ds. $$ Note that this is ...


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There is no difference in information, though the fitting algorithm may increase in complexity. First note that in practice you never have an entire curve or surface of prices $C(K,T)$ of any kind of option. You only have a finite number of observations and even those typically have a bid and an offer. I would therefore argue that the correct picture of ...


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The Price of an American option may contain information on the expected behaviour of it's holder. When might he/she exercise the option ? Contrary to European options that don't. Thus when you are primarily interested in "reconstructing" the transition density - I would stick with the European-Option-Prices. If however you were to price path dependant ...


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The easiest way is to use single-expiry volatility that you would get from your volatility surface. It is usually good enough for government work (e.g. to get a sense if you are getting raped by a dealer or to understand your vega risk). A better way is to use local volatility model and the whole volatility surface up to the date of expiry. There is also a ...



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