= Cox-Ross short-rate pricing equation
{c}
{title2=$V_t+(b-\sigma\theta)V_r+\tfrac12\sigma^2V_{rr}-rV=0$}
For smooth derivative prices depending on a <Markov> <short rate>, <Itô formula> gives physical drift $m=V_t+bV_r+\sigma^2V_{rr}/2$ and exposure $s=\sigma V_r$. The common <short-rate market price of risk> gives $m-rV=\theta s$, yielding this equation. Under the <risk-neutral measure>, the rate drift is $b-\sigma\theta$ and the bank-discounted price is a <martingale> under suitable integrability. A unit <zero-coupon bond> has terminal value one and price $\mathbb E^Q[\exp(-\int_t^T r_sds)\mid r_t=r]$.
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