Why a Call Spread’s Value Curve Can Be Asymmetric Before Expiry

Summary

The document asks whether a call spread’s value plotted against the underlying price must be symmetric before expiration. The response distinguishes the payoff at maturity from the option’s value earlier in its life. At maturity, the spread’s payoff may appear symmetric in the referenced plot, but an earlier value curve depends on the distribution used to model the underlying.

The explanation says symmetry is expected only when the underlying’s probability density is symmetric, giving a normal distribution as an example. A lognormal model, commonly used for positive asset prices, has a skewed density and can therefore produce an asymmetric value curve. This is a qualitative explanation rather than a derivation or numerical example, and it assumes the plot shows option value against underlying price. The document does not specify the spread’s strikes, pricing parameters, or other model details needed to assess a particular graph.

Key ideas

• A call spread’s value curve before expiry need not be symmetric.
• Symmetry depends on the modeled distribution of the underlying price.
• A symmetric density, such as a normal distribution, can lead to a symmetric curve.
• A lognormal density is skewed and can lead to an asymmetric curve.
• The explanation assumes the graph plots option value against underlying price.

Tags

# Does a Call Spread always need to be symmetric?


# Does a Call Spread always need to be symmetric?












I have a plot of a Call Spread Option at time $t ={0}$ but the graph of the call spread is not completely symmetric. My question is: does it have to be? Here is the plot I'm referring to:

I'm just wondering because at maturity time the Call Spread becomes symmetric, so it anyone can provide a bit of information on this I'd really appreciate it. Thanks!

## Answer by dm63 (score 4, accepted)

https://quant.stackexchange.com/a/26175

I assume this is a plot of option value versus price of the underlying. The only case where it ought to be symmetric is if the pdf of the underlying is symmetric eg normally distributed. I'm guessing your chart assumes a lognormal underlying, which is a non symmetric pdf, so the graph is non symmetric.

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