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Practitioners tend to wear Black-Scholes glasses when dealing with European options: to them, quoting a certain option price today $V(S_0;T,K)$ is equivalent to quoting the forward price of the underlying $F(0,T)$ along with a relevant Black-Scholes volatility figure $\sigma(T,K)$(*) That being said, when you are asked to price a European option on a stock $...


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One assumption is that both (or more) instruments are liquid enough to offer a market (both sides). You can use the bid/ask/mid (your choice) or "conflate" (implemented by the big boys on their data feeds). i.e. 1 second conflation: if no trade, send out last trade price (or assume so in your application).


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I wrote a paper with Alex Shubert. You can get it on archive.org.


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Humm....you must miss some hypothesis. Assuming $\alpha>0,\beta>0$, you can without loss of generality set $\alpha=1$. (since $\frac{r}{\alpha}$ and $\frac{V}{\alpha^2}$ being positively correlated is the same as $r$ and $V$ positively correlated) now, positive correlation is equivalent to positive covariance. Working with covariance and above ...



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