ZBC and ZBP can be used to price caps & floors since they can be viewed as portfolios of zero-bond options:
\[Cap(t,T,N,X) = N \sum_{i=1}^{n}[P(t,t_{i-1})\theta(-h_i + \sigma_p^i) - (1+X_{Ti})P(t,t_i)\theta(-h_i)]\]
\[Flr(t,T,N,X) = N \sum_{i=1}^{n}[(1+X_{Ti})P(t,t_i)\theta(h_i)-P(t,t_{i-1})\theta(h_i-\sigma_p^i)]\]
The terms are derived from:
\[{\sigma_p^i} = \sigma{\sqrt{\frac{1-e^{2a(t_{i-1}-t)}}{2a}}}B(t_{i-1},t)\]
\[{h_i} = {\frac{1}{\sigma_p^i}} ln (\frac{P(t,t_i)(1+X_{Ti})}{P(t,t_{i-1})}) + \frac{\sigma_p^i}{2}\]