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The SABR model represents the stochastic evolution of the price of some kind of assets under the measure for which it is a zero-drift martingale. For Forward contracts it's the so called "Forward measure", the one induced using the price of a zero-coupon bond that matures at the forward contract payment date as numeraire. Now there is a difference ...


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Usually the the difference between your average price between $t_0$ and $T$ and the price at $t_0$ is called the Implementation Shortfall (IS). They are a lot of references to do this, just cite these two ones: Market Impacts and the Life Cycle of Investors Orders, by Bacry, Iuga, Lasnier and L Modelling Transaction Costs When Trades May Be Crowded: A ...


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What are common methods to compute implied volatility index? One could use VIX method on other underlying. Yes, the CBOE offers this for Apple, Google, Amazon, Goldman Sachs and IBM (see here). In my working paper here I use the CBOE VIX methodology on a sample of 268 individual equities in the same way. It also includes a comprehensive derivation of the ...


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If you are predicting lower one year volatility than the options are pricing in, sell one year options on the underlying that you think will be lower and hedge the delta. If you are predicting higher one year volatility than the options are pricing in, buy one year options on the underlying that you think will be higher and hedge the delta. Your hedging ...


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Use calendar spreads. If implieds are high vs your prediction, sell short dated straddles, buy longer dated straddles, vega neutral. If implieds are lower vs your prediction, buy short dated straddles, sell longer dated straddles, vega neutral. Your short dated straddles will have more gamma (and theta) than your longer dated straddle positions and ...


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You will want to buy the 10 delta calls and puts vs selling the at-the-money calls and puts when implied volatility is high vs your view on realized. You are selling vol which means that your view is that volatility will be lower than that implied by the markets (your maximum profit will be if the underlying doesn't move (no volatility) and you end up ...


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This resource surveys the main available replication-based approximations of discrete variance swap pricing: continuous method Derman's method Trapezoidal/Simpson methods Optimal Quadratic Hedge (Leung and Lorig) Edit: We have: $$ A_{m,n}:=(t_n-t_m)^{-1}\sum_{i=m+1}^n R^2_i = (t_n-t_m)^{-1}\left(\sum_{i=1}^n R^2_i -\sum_{i=1}^m R^2_i\right) $$ $$ = w_1 (...


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Althoug I can only provide recommendation as to the forecasting task (see below), I want to point out one big caveat one has to account for: Intraday price volatility- or to be exact, the absolute returns, exhibit an intraday pattern which looks like a wave. This implies that the data is autocorrelated, which violates the assumptions of ARCH/GARCH models (...


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I was thinking of simply limiting set of options that go into computation to K0 strike+ 1 option on each side (cboe.com/micro/vix/vixwhite.pdf). Not sure if this is a good idea though. Hence the question If you have a full/complete options chain then naturally to calculate the VIX you should use the VIX formula, which should be interpreted as a definition. ...


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This issue with using a kernel to estimate a quantity for a one-minute bin is that you can write $\xi^2$ as $$ \hat\xi^2 = \frac{\overline{RV}_{\text{dense}}}{\overline{RV}_{\text{sparse}}}. $$ The estimator $\overline{RV}_{\text{sparse}} \approx\widehat{IV}\approx \sqrt{T\int_0^Y \sigma_u^4 du}$ samples returns sparsely. The idea is that the sampling period ...


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A simpler answer is thus. There are known historical values for the past year for the mean. It's simply the end of year value divided by the beginning value. However, we can't improve the estimate of the mean by looking at, say, the daily returns and aggregating them up to 250 days of trading to make a better estimate of the mean (return): it will simply ...


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