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So, I'm trying to simulate a correlated double exponential jump process for two assets, and I understand the pure exponential jump process ($\eta_1$ and $\eta_2$, the probability of an upward jump occurring, the size of the jump, etc, etc), but it's trying to correlate the two jump occurrences that's confusing me.

For example, correlating normally distributed jumps processes is tractable, where $n_{t}^{i}$ are distinct Poisson processes, and $K_i$ is relatively easily computed, enter image description here

However, for the double exponential, the best resource I've found is here on pg. 40, but its explanation is quite frankly inscrutable. Could anyone explain to an advanced beginner how this could be simulated? Even pointing toward some successful simulation code would go a long way.

Thank you to all in advance.

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  • $\begingroup$ Not clear what you want to correlate, is it the Poisson random variables, or the intensities of the jumps? If it's the first, please refer to: math.stackexchange.com/a/244999 $\endgroup$ – byouness Jun 6 '18 at 1:22
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I don't think you can correlate discrete processes in the traditional sense.

Instead, I would make the two Poisson intensities time-varying through which a degree of "jump similarity" can be injected

Say each jump intensity is a positive mean reverting process, such as an exponential OU, where the increments are jointly distributed (I.e. with correlation)

Now when one jump intensity moves up, you can influence the other, but know the intensities are always positive and never drift off too high

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