# Tag Info

The relationship between theta and gamma is the Black-Scholes PDE. Let's take normal B-S dynamics with $r=0$: $dS_t = \sigma S_t dW_t$ The pricing PDE for a derivative $g(S_T)$ is (with terminal condition $g$): $\frac{dp}{dt} = \frac{1}{2}\sigma^2S^2 \frac{d^2p}{dS^2}$ Or $\Theta = \frac{1}{2}\sigma^2S^2 \Gamma$ This PDE has a solution (Feynman-Kac Theorem): ...