Log-Double-Uniform Jump-Diffision Model for Stock Price Dynamics (Working Paper)

where a < 0 < b and 0 < p < 1 represents the probability of downword jumps and q = 1− p is the probability of upward jumps. The set indicator function is I{S} for set S. The mean of Q is μj = 1 2 (pa + qb) and the variance of Q is σ j = pq 4 (b− a) + pa2+qb2 12 . The third central moment of Q is M (3) j ≡ E[(q − μj)] = pq 4 (b − a)(aq + bp) and The fourth central moment of Q is M (4) j ≡ E[(q−μj)] = μj+p/5(a−5aμj+10aμj−10aμj)+q/5(b−5bμj+10bμj−10bμj ). According to the Itô stochastic chain rule [5] for jump-diffusions, the log-return process ln(S(t)) satisfies the constant coefficient SDE