Option bounds for multinomial stock returns in Jump-Diffusion processes - a Monte Carlo simulation for a multi-jump process

This paper addresses the problem of option bounds computation under the assumption that the price of the underlying asset follows a jump-diffusion Merton process as formulated in Perrakis (1993) extending the number of the jumps from one jump up and one jump down with fixed sizes to a finite number of jumps with sizes drawn from the lognormal distribution. The objective of this paper is to create a Monte Carlo simulation for the estimation of the bounds with various numbers of jumps and periods to maturity.