We all know that the butterfly spread no-arbitrage condition can be expressed as an inequality restriction on the second-order derivative $\partial ^2C/\partial K^2 \geq 0$, which also means the market implied risk-neutral density is non-negative under no-arbitrage condition, following Breeden-Litzenberger result.

My questions is: is there a way that we could express the calendar spread no-arbitrage conditions in the pdf terms?

Many thanks in advance!


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