# Tag Info

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No. Implied volatility isn't a historical measure of standard deviation. Implied volatility is used to relate a market price to some model, be that Black-Scholes or something more sophisticated. Another way to phrase it, implied vol is that single vol input into a model, such that the model reproduces the market prices. Different models will have ...

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After a lot of guess work, I think can try and answer what I think might be your question. First, note that at maturity the forward equals the spot: $F_T^T = S_T$ so I am not sure what you mean by "forward price strike". I think you mean that your have forward prices of calls and puts. If you chose a model for your index $S$ and the rates, then the ...

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A pithy way to put it is "implied volatility is the wrong number to put in the wrong formula to get the right price." That is, implied volatility is by definition the parameter $\sigma$ to plug into the Black-Scholes option pricing formula to get the market price of a vanilla option. This is called "volatility," but in reality it isn't the same as the ...

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In the link you provided, by noting the construction of array p[], p0 and p1 are respectively the discounted $\texttt{down}$ and $\texttt{up}$ probabilities. Since $d=\frac{1}{u}$, then \begin{align*} p0 &= e^{-r \Delta T}\, \frac{u-e^{(r-q)\Delta T}}{u-d}\\ &= \frac{\big(u\,e^{-r \Delta T} -e^{-q\Delta T}\big)u }{u^2-1}, \end{align*} and ...

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My 10 cents is the formulas aren't super intricate: they attempt to reflect certain realities. At the simplest level, simply intrinsic value + time value. You could make up your price just from that. But if you did just intrinsic value + a time value and put your price out there then you face the EMH risks, and if your price is off market you'd get ...

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A first usage that you already probably thought of is that the markets are not perfectly efficient, so the options are slightly mispriced. Then you need to know in which side you should invest. And that is true, most option contracts are not liquid enough to be perfectly priced by the markets. Other use is when you issue a new option (for example if there ...

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