How Implied Volatility and Time Affect a Put Backspread’s P&L

Summary

The document discusses a put backspread, described as selling a higher-strike put and buying a lower-strike put with the same maturity. At expiration, the payoff has a V-shaped profile. In the answer’s simplified description, the steepness of that payoff is determined by position notionals: buying more of the lower-strike puts makes the relevant side steeper.

Implied volatility and time to expiration affect the strategy’s value before expiration through the cost of the options. Higher costs for the long options, relative to the short option, make the position more expensive to establish and shift its P&L profile downward. More time generally adds cost, all else equal. The answer does not quantify these effects or address changes in interim Greeks, skew, rates, or other market conditions, so its claims describe broad intuition rather than a complete risk analysis.

Key ideas

• A put backspread sells a higher-strike put and buys one or more lower-strike puts with the same maturity.
• The V-shaped payoff described in the answer is the expiration profile.
• Position notionals determine the steepness of that expiration payoff in the simplified setup.
• Volatility and time affect option costs and therefore the strategy’s pre-expiration P&L level.
• The discussion gives qualitative intuition and omits a full analysis of interim risk sensitivities.

Tags

# On P and L of backspread


# On P and L of backspread












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

## Answer by AKdemy (score 1, accepted)

https://quant.stackexchange.com/a/65887

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.