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I am trying to understand the pricing of various types of swaptions.

Suppose I have a swap that starts in 3 months time. How would I go about pricing a swaption on this swap in the following cases:

1 Month option 2 Month option 3 Month option

I know the standard theory, which seems to let me price the swaption for a 3 month option. However I can't seem to figure out how to bring in the forward starting arrangement for the 1 and 2 month option.

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The Black 76 swaption formula works for all these cases. The expiration time T= 1mo, 2mo or 3mo but the forward rate of the swap is the same in each case. The market will place different implied volatilities on these 3 options, according to the expectations of realized volatility in these 3 time periods.

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