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2

If you have a Bloomberg terminal, you can lookup vols for different currencies and indexes with the VCUB function, where you can check the raw market input data and the surface construction parameters (vol type, interpolation, calibration, tenors, etc) and output. You will have to have a Bloomberg licence because they don't really "offer" this data ...


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There are a number of ways to look at this: BSM model vega: $$Vega_{call}=Se^{-q\tau}\phi(d_1)\sqrt{\tau}$$ Now if you buy the arguments and assumptions of the model, that means it must be positive mathematically. No matter the value of $$d_1 = \frac{\log\left(\frac{S}{K}\right) + (r-q+\frac{1}{2}\sigma^2)(T-t)}{\sigma\sqrt{T-t}},$$ the value of $\phi(d_1)\...


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I think all the previous answers have small mistakes: Given that you have derived the return over the period of interest, i.e. in your case 2009-2020 we can then: Compute the return at the granularity level of your data i.e: $r_{quarterly}=(1+r_{total_{period}})^{\frac{1}{number_{datapoints}}}-1$ This is then the return of the whole period on a quarterly ...


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How to find optimal $K$? If we let $i$ for $i=1,\ldots,n$ be the amount of intraday returns over a fixed interval $T$ (one day in empirical applications), then in Zhang et al. (2005) (p. 1397) specified above, they tell you that the optimal $c$, can be obtained via the equation: \begin{equation} c^{*} = \left(\frac{T}{12 \cdot \left(\mathbb{E}\left[\...


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There are no no-arbitrage conditions on ATM vols of swaptions with different expiries/tenors, because the underlying swaps forward rates are different instruments. There are conditions however for these vols to be compatible with specific IR models. For instance when calibrating a Hull & White model on a set of coterminal swaptions, it sometimes happens ...


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The TLDR; to your question: How can one use realized volatility as a volatility model to do out-of-sample prediction? You extended known models to incorporate additional information procured from high-frequency data. Going from the vanilla GARCH to a realized GARCH model can be done by adding an auxiliary model as an external regressor that captures ...


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