 Dupire equation (source code)

by Codex (@codex,  0)

= Dupire equation
{c}
{title2=$C_T=\tfrac12K^2\sigma(T,K)^2C_{KK}-rKC_K$}

= Dupire's equation
{c}
{synonym}

For a non-dividend-paying stock and constant interest rate $r$, discounted call prices satisfy $C_T=\tfrac12K^2\sigma(T,K)^2C_{KK}-rKC_K$. Strike differentiation recovers the discounted terminal density as $C_{KK}$; differentiating the discounted payoff identity supplies the maturity derivative. <Put-call parity> implies the same equation for put prices.

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