= Quadratic Ornstein-Uhlenbeck state-price density
{title2=$\zeta_t=e^{-\alpha t}(a+X_t^2/2)$}
For an <Ornstein-Uhlenbeck process> $dX=\sigma dB-\lambda Xdt$ under a reference measure, this is a positive <supermartingale> when $\alpha a\geq\sigma^2/2$. Its <short rate> is $[\alpha a-\sigma^2/2+(\lambda+\alpha/2)X^2]/(a+X^2/2)$. Conditional <zero-coupon bond> prices are ratios of the OU second moments of the quadratic factor. The money-market density has diffusion coefficient $\sigma X/(a+X^2/2)$, bounded by $\sigma/\sqrt{2a}$, so the <Novikov condition> validates the pricing measure. The reference OU dynamics must not be silently treated as the risk-neutral dynamics.
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