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You could model the forward Libor Rates using Libor Market Model in a Monte Carlo setting to get the Libor behavior in the future.

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from a practitioner perspective, i can say there's no such thing as a 0 year swap (obviously). The shortest tenor that you could trade would be a contract on one month LIBOR or more likely 3 month LIBOR. Then the instrument you are asking about is a 5 year expiration caplet (payoff in 5 years = max (0, LIBOR- strike).)

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We consider a single Libor rate. The application to a swap is straightforward. Consider the Libor calculation period $[T_1, \, T_2]$ and the Libor payment made at $T_1$. We denote by $\Delta = T_2-T_1$ the length in years of the calculation period. Here, we ignore the two-day payment delay as its impact to pricing is immaterial. We assume that, under the ...

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You understand that forward curve can replicate the payment on FL at the next reset date. Therefore, the vanilla swap can be valued as a series of FRA - meaning, you assume that the forward rate will be realized and the resulting cash flow can be discounted to the present using the zero swap curve. When you have a non-standard situation, like for an ...

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lets take it as simple that all payment are at the same time. When you want to calculate the floating, you always look at the previous period. But to calculate the first payment, we do not have forward rate at time t=0. But when you want to calculate between two periods, you have forward rates and you can always fix the rate for next period (floating one). ...

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