Consider a swap with reset dates T₀,T₁, ··· ,T_n−1 and payment dates T₁,T₂, ··· ,T_n. A trigger swap is a contract where the holder has to enter into a swap with fixed swap rate K over the remaining period [T_i,T_n] when L_i(T_i) > K_i, where K_i is the trigger level set for date T_i. Define i^∗ to be

Here, T_i∗ is a stopping time. For t 1 show that the time-t value of the trigger swap can be expressed as

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= min {m Lm (tm) > Km}. 1