Merton's jump diffusion model


Added Merton76.pdf to papers. He specifies a compound Poisson process with normally distributed jumps.

The model replaces Brownian motion with
X(t) = B(t) + sum_{T_j < t} N_j, 
where N_j are independent normal mean 0, variance tau^2, lambda is the Poisson jump intensity, and T_j are the jump times. Note E X(t) = 0.

Find a formula for E(k - F(t))^+ having the form sum_j c_j E(k - F_j(t))^+ for appropriate constants c_j and lognormal F_j. Recall F(t) = f exp(-s^2 t/2 + s B(t)).