CDO Tranche Valuation with Systemic Risk Simulations

Summary

The document asks how to illustrate the effect of model assumptions in a systemic banking-risk framework on a collateralized debt obligation payoff. The motivating setup is a mean-field model of institutional distance to default, with dynamics affected by drift, volatility, and contagion. The proposed exercise varies features such as whether contagion depends on the survival measure and whether contagion between institutions is weak or strong, then uses simulated losses as an example application.

The question raises two valuation issues without resolving them: whether a single-tranche payoff can be represented by subtracting expected loss from the maturity payment, and whether averaging simulated loss paths is sufficient. It also asks how a risk-neutral martingale measure should enter the simulation. No payoff formula, pricing procedure, or simulation results are provided, so the document is best read as a set of modeling and valuation questions. In particular, it does not establish that an ordinary mean of simulated losses produces a risk-neutral CDO price.

Key ideas

• The proposed systemic-risk model links institutional survival dynamics to drift, volatility, and contagion.
• Model scenarios could vary contagion strength and how contagion depends on the survival measure.
• The document asks whether expected tranche loss alone captures a single-tranche CDO payoff.
• It also asks how Monte Carlo loss estimates should incorporate a risk-neutral pricing measure.
• No valuation answer or simulation evidence is given.

Tags

# Calculating CDO pay-off


# Calculating CDO pay-off












Background 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.

Problem/Question

- 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?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.