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3

You can show that "the implied variance of an ATM short maturity option is equal to the expectation under the risk neutral measure of the integrated variance over the life of the option." As you move away from the assumptions: ie not ATM, longer maturity, risk neutral measure far from true, then the forecasting power diminishes. (Google 'stochastic ...


3

I would say that $\log K/F$ points towards a log-normal type model. If I were you I would experiment with the moneyness defined as $K-F$ instead. This would make it consistent with normal dynamics. An alternative would be to define an 'interest rate floor', say $L=-200bp$ and take relative changes relative to that rather than zero, ie define moneyness as ...


2

Yes, your broker could have used one or combination of many factors: estimated volatility surface from historical returns of your target index, historical returns of similar indexes, implied volatility of similar indexes, existing inventory,etc. Check out these two approaches to deriving surfaces from returns starting slide 14


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1 is wrong. The implied vol is a convenient way to look at the option price, nothing more. 2 is an observed fact for equities in general but not the case for some other assets eg commodity futures. 3 is also an observed fact for equities generally (but not for single stocks with short time to expiry). If 1 and 2 were true, then 3 would naturally ...


1

To my point of view, the answer is hidden in your question. You correctly stated some of the BS assumptions and empirically it is proven that they are not true (volatility is not constant and the assumption regarding the distribution of returns is unrealistic due to fat tails). The model is as good as its assumptions are. Given that volatility is the ...


1

Well, hopefully your calculations are right. There are a few things to remember: The carry can be higher than what you are thinking. Very often you will get charged if you are long or short. That can cost a lot depending on the name. Implied is theoretically always higher than realized. You are selling insurance. You should collect a premium more ...


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Well... this is simply a picture to illustrate what is written in the text. It is not an absolute truth. The author just chose 2 implied volatility smiles that share the same ATM volatility level for clarity. One exhibits negative skew (typical of equity markets) and the other one is flat (you'll never observe that in practice, although it is exactly what ...



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