I got a model for the distance-to-default of an instution in a system of banks from the paper "An SPDE model for systemic risk with endogeneous contagion". Therein they postulated that the empirical survival measure converges to a mean field limit. The SPDE describing this mean field limit depends on the drift and a contagion term w.r.t time $t$ and the volatility w.r.t a Brownian motion. To illustrate what influence the contagion term and some other specifications of the model have, I'd like to simulate, what happens when one changes the nature of those single parameters (e.g. they can depend on the survival measure, they can be constant, contagion between different instutions can be very high or very low). This simulation should include an example where it can be used, for example in the calculation of the pay off of a CDO.
To get a proper illustration, does it suffice to consider a single-tranche CDO, simply calculate the expected loss and then substract it from the amount of money that should be paid back to the buyer at maturity (Or is there more to the pay-off function)?
When simulating it, does it suffice to simulate $N$ realizations of the loss process and calculate the mean? Or how do I include a risk-neutral martingale measure?