\(C = S N(d_1) - K e^{-rT} N(d_2)\) \(P = K e^{-rT} N(-d_2) - S N(-d_1)\) \(C - P = S - K e^{-rT}\) \(dS_t = \mu S_t dt + \sigma S_t dW_t\) \(\hat{\beta} = (X^\top X)^{-1} X^\top y\)