They are fantastic, the whole gypsy-wannabe thing - "On rêve de Bohême, de routes, de Romanichels, mais en fait on s'appelle Romain, Michel"
"Gypsy for one day" is pretty groovy. This formula looks a bit hairy now that I think about it. Before I try and write up a more precise formula, why is it that we have "a trade off between (iv vs rv) and (iv vs fv)"? can we not have both fv and iv gains? Ie we put on a calendar and the stock does not move for 30 days and the back month spikes in vol (due to some event).
The assumption (a reasonable one) is that realized and implied volatilities are somewhat correlated. Situations when you make or lose money on both legs (based on event pricing, a relief rally or other) are rather rare. Btw, I have mixed up the directions - it should be vegaFront*(RV-IV).
What does the SPX volatility surface look like? My understanding is that longer-dated atm options would tend to have higher IV and lower gamma. The funny thing with calendars is that gamma can flip from positive to negative while vega can change sign.
Could you give an example of a vanilla calendar (same strike, same notional for both legs) where Vega would change sign?
Although this is not an essential condition raw vega or weighted vega can change sign or reverse. Difficult to give examples, my opinion comes from observation. Two dimension representaion is irrilevant.
If you have a vanilla calendar and it changes it’s sign for raw Vega, that means that either initial or current forward volatility was not arbitrage-free. That’s, ahem, very unlikely. The only IRL situations where I have seen something like that happening is in case of impending bankruptcy proceedings or takeover