= Gaussian caplet bond-put formula
{c}
{title2=$C_t=\Phi(-d_2)P(t,T)-(1+\delta K)\Phi(-d_1)P(t,U)$}
For a <Gaussian forward-rate field> with deterministic volatility, put $F=P(t,U)/P(t,T)$, $K_b=(1+\delta K)^{-1}$, and $v^2=\int_t^T\|\Sigma(s,U)-\Sigma(s,T)\|^2ds$. Under the <T-forward measure>, $F$ is lognormal with that integrated variance. With $d_1=\log(F/K_b)/v+v/2$ and $d_2=d_1-v$, the displayed expression is the <caplet> price. At $v=0$ use the discounted intrinsic bond-put value. Gaussian instantaneous rates do not make the reset floating rate Gaussian; the exponential bond relation is what yields this bond-option formula.
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