FinStream

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0DTE4 : More detail. Calibrate typical date. The first 9-32:00 timestamp fails to calibrate due to odd data. Usually ok. Also we see put-call violated in my data set at times so I guess need to be careful of a snap shot. Just looking to see that the LHS becomes more like a smile at we approach expiry. It does as it should. My stochastic QD model close to SVI here on 0DTE (less so in BTC but will get back to that). Calibration and metrics out 30min to expiry not too bad.

0DTE:3  Skew Risk Premia Exists Taken for granted it seems. We know the SPX price returns are fat-tailed and that should be reflected in a skew strike relationship in the option pricing formulas. But the ODTE's also contain information about investors’ risk preferences and risk premia over intra-daily horizons. So they are entangled somewhat. We form the intraday density from the option prices and obtain quantiles. Now we know this is RN density and thus I'm not trying to forecast prices. But lets suppose that the skew we see has very little risk premia, hedging pressure premiums etc. Then we should see the final spot appear within the quantile bands at some expected rate reflective of its actual price dynamics. However if the skew has a significant RP then these quantile bands are partially fictitious as the RP doesn't actually influence the final spot 0DTE to any extent. So we should see that the low price quantile buckets are less populated than expected. This is what we see.  It changes over time and some risk aversion on the call side can be seen. And some days seem weird. A larger set be collated.(1mth below as an example) In the histogram the blue (actual counts) are less than expected and move to the right which is highly suggestive of a skew risk premia. The skew is just to steep. We can probably un-entangle (not sure that is a word) the 2 effects

BTC 14thOct: Note: There RE 3 QD metric images. I won't always show fittings, it is more about gaining comfort in them given that it is very hard to fit stochastic models 1-5 days. Try it and you will know why. As stated before pretty sure the vols are parametric but anyway they are very mean looking. But good fits it allows to use the density function. Certainly the Sept26 LHS skew has diminished some what and RHS skew much higher. Interestingly the embedded risk premia has changed sign over the last week and is more 'normal'. More Call like. We present what we think are the appropriate RR(25) and BF(25) values. Don't know what you are seeing but if it above my values I reckon they are overvalued and vice-versa. We present the Variance Swap Strike rate as well. Might be useful metric in time. Will try and provide some more commentary on the QD model soon once it is bedded down so to speak. The model predicts a convenience yield and spot state dependent, as a consequence of arbitrage and is not imposed, which is super cool (in commodities as well not that BTC is one). I'll try and see this empirically once I accumulate more data

We calibrate the QDT (fat-tailed) model and obtain the risk-neutral density. From that density we integrate to get option prices across strikes (no Black needed). We then invert Black to express those prices as implied vols. Using a chosen delta convention (e.g., forward delta), we locate the 25Δ call/put strikes, read their implied vols, and compute RR(25) and BF(25). Note that RR/BF are model- and convention-dependent because the 25Δ strikes are selected using a model’s delta and tail shape. The reported RR/BF are therefore QDT-fair quotes under the stated Black forward-delta convention—so others can compare on a consistent basis (differences vs. desk marks mainly reflect tail and extrapolation choices).