Extension of GBM with a compound-Poisson jump term: dS_t / S_t- = (μ - λ k)dt + σ,dW_t + (Y_t - 1),dN_t, where N_t is Poisson with intensity λ, jump sizes ln Y_t sim mathcalN(μ_J, σ_J^2), and k = mathbbE[Y - 1]. Closed-form option price as a Poisson-weighted sum of BSM prices: C = sum_n=0^∞ dfrace^-λ' T(λ' T)^nn!,C_BS(σ_n, r_n). Generates short-dated implied-vol skew that diffusion alone cannot.