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Does anyone know how the P and L on put backspread changes as a function of implied volatility and longer expiration?

One wants as much gamma as possible as far as I understand, in turn being related to the steepness of the "V". Is it possible to say something about how the shape of the "V" changes with expiration and IV? and are the other things to consider when controlling this shape

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The V that you see is only at expiry (like any hockey stick) and completely independent of vol or tenor. All that matter is notional. Assuming put backspread, you sell a put with higher strike, and buy it back with lower strike(same maturity). The more you buy the steeper.

Vol will only impact the position of V. The more expensive the long positions are, the more the strategy costs & the more it shifts the entire graph down. This depends again on N, but also directly on the vola of long vs short positions. Similar for more time. More time means more cost (all else equal).

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    $\begingroup$ A backspread has usually (or always?) a positive Vega, so it profits from increases in IV during its life (before it expires). However you cannot analyze this by looking at the payoff diagram at expiration, at that time IV no longer matters. $\endgroup$
    – nbbo2
    Commented Jul 6, 2021 at 1:07
  • $\begingroup$ @noob2 what does this imply? $\endgroup$
    – user123124
    Commented Aug 8, 2021 at 6:13
  • $\begingroup$ Some people who predict a crash buy backspreads with the idea that when the crash happens and IV soars they will sell the position for a juicy profit (due both to lower S and higher IV). If they sell too late the profits will be somewhat reduced as IV normalizes. $\endgroup$
    – nbbo2
    Commented Aug 13, 2021 at 9:12

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