What does the payoff diagram look like for a long payer swaption corridor?
For example, suppose that I am looking at a long-payer $1 \times 10$-year swaption with 10Y swaps as the underlying. If I am buying a 2.0% strike and selling a 2.5% strike, I'm trying to plot the payoffs at various future potential 10Y swap rates in one year (e.g. 1.5%, 2.0%, 2.5%, 3.0%, $...$). I haven't found a good example online (and am having trouble calculating in excel) and am concerned that the convexity of the bonds will make the payoff nonlinear as the 10Y market swap rate in one year increases above my high strike (unlike IR caps). If it is nonlinear, is there a quick, intuitive explanation?
Any thoughts/guidance would be appreciated. Thanks.