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Here is a example of Cap option in John Holl's book Options, Futures and Other Derivatives 9th page 681.

One thing I am confused that there are two discounted rate, one is LIBOR/swap zero curve is flat at 7% and the other is The continuously compounded zero rate for all maturities is 6.9395%.

Here we use forward price $F_k,$ it seems we should use the LIBOR as the a discounted rate.

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7% annual LIBOR with quarterly payment = 4 * 1.75% coupons

1.0175 ^ 4 = 1.071859

ln(1.071859) = 6.9395%, the continuously compounded rate.

This is the second question you ask about converting yields with different quoting conventions, I suggest you read some literature about this before attempting more complex equations. By the way it's John Hull, John Holl is writing beer guides.

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