The price at time t of a European Call option with strike X, maturity T on a discount bond maturing at time S is given by:
\[ZBC(t,T,S,X) = P(t,S)\theta(h) - XP(t,T)\theta(h-\sigma^{p})\]
The price at time t of a European Put option with strike X, maturity T on a discount bond maturing at time S is given by:
\[ZBP(t,T,S,X) = XP(t,T)\theta(-h+\sigma^{p}) - P(t,T)\theta(-h)\]
The terms are derived from:
\[{\sigma^{p}} = \sigma \sqrt{1 - \frac{e ^ {-2a(T-t)}}{2a}} B(T,S)\]
\[h = \frac{1}{\sigma^{p}} ln(\frac{P(t,S)}{P(t,T)X}) + \frac{\sigma ^ {p}}{2}\]