Monte Carlo Simulation of Spread Strategy. Two correlated assets vs One spread simulation?

I am trying to simulate paths of a certain spread strategy such as a calendar spread between two futures ( May Crude vs Aug Crude) using a Monte Carlo simulation.

My questions is there a difference between modeling two correlated paths using both price histories, then taking the difference between the two simulations, or simply using the historic spread price to simulate one path? If so what are the differences, pros and cons between the two?

• So the question is, "What's the difference between: (1) simulating the vector-stochastic process $(x_t, y_t)$, then computing $\Delta_t = y_t - x_t$ and (2) more directly simulating stochastic process $\Delta_t$? – Matthew Gunn Feb 28 '18 at 15:53
• Yes, that's probably the more mathematical way to pose the question. – bronson Feb 28 '18 at 16:05