= Call-price density recovery
{title2=$C(K)=f_Q(K)$}
= Breeden-Litzenberger density formula
{c}
{synonym}
In a zero-interest one-period market with a continuous terminal <stock> law under a pricing measure, $C(K)=\mathbb E_Q(S-K)^+$ implies $-C'(K)=Q(S>K)$ and $C''(K)=f_Q(K)$. Thus a full differentiable call curve determines its pricing density. A finite collection of strikes generally does not. With a deterministic nonunit <discount factor>, divide the call curve by that factor before recovering the probability density.
Back to article page
