MertonJumpModel

Merton jump-diffusion as a composable step block (Seam 5):

dS/S = (r - lambda kappa) dt + sigma dW + (Y - 1) dN
ln Y ~ N(muJ, deltaJ^2)
kappa = E[Y - 1] = exp(muJ + deltaJ^2 / 2) - 1

Each step draws a diffusion normal and, from a uniform, a smoothed indicator 1{U < lambda dt} for at most one jump (exact as the monitoring gets fine, since P(>= 2 jumps per step) = O((lambda dt)^2)). The jump count is not differentiated; muJ, deltaJ and the compensator are, so one adjoint sweep returns the jump-parameter risk next to the spot / vol / rate Greeks.

Validated against the exact MertonJumpDiffusion Poisson-series price (agrees to Monte-Carlo error). The smoothed jump indicator leaves an O(0.1%) martingale bias in E[S_T] — negligible for option prices, visible only in a put-call-parity check at high path counts — that shrinks with the indicator width.