Ratchet caps have a similar structure as standard caps. The main difference is that while caps have a fixed caprate for every caplet, for ratchet caps we will have a variable caprate dependent on earlier LIBOR resets for every ratchet caplet plus a spread.
The price of a ratchet cap with notional \(N\), spread \(s\) and initial spread \(\kappa_0\) is given by the following formula:
\[RCap = \sum_{i=0}^{n}RCaplet(i)\]
\[RCaplet(i) = \tau_iN(L_i(T_i)-K_i)^+\frac{B(0)}{B(i+1)}\]
\[\begin{split}K_i=\begin{cases}s+\kappa_0 & i = 0\\L_i(T_i)+s & i > 0\end{cases}\end{split}\]
\[B(t) = [\prod_{k=t}^{n}(1+\tau_kL_k(t))]^{-1}\]