![]() ![]() In other words, what default correlation allows us to do is to establish the size of this intersecting common area of joint default given known marginal probabilities. The way default correlation works is that the larger the default correlation, the greater is this area, or the greater is the overlap between the two circles. It is the size of this area that is determined by the default correlation. Their intersecting areas represent the space where both the securities default together. Each circle represents the marginal probability of the default of the individual securities (note: by ‘marginal probabilities’ I mean the standalone probability of default of the security regardless of the default or otherwise of the other security). The three cases above are depicted below. In such a case, the default correlation is zero, or very close to that in the hypothetical scenario described above.Īn easier way to think about this is using Venn diagrams. The third scenario represents a situation where the defaults of the two securities are completely random, and happen regardless of what happens to the other security. The calculation of the correlation itself is done using the Excel formula ‘CORREL’, which I have illustrated in the graphic above. ![]() These are the two extreme, or limiting cases, and are useful as they quite easily illustrate what default correlations of +1 and -1 mean. The second scenario represents the other extreme where survival by one certainly implies the other will default, or the other way round. So the first scenario is one where the securities survive or default in lockstep with each other, ie, when one defaults, the other one does too, and also vice-versa. Consider each of the observations below as having been the outcome of the passage of time on the default or survival of our two securities in 20 identical but parallel universes – a concept that might be quite easy to think about if you grew up watching the original Star Trek). We don’t know in advance what that realized observation will be. Once time has passed, the security will either have defaulted or not. (of course, in real life, there is only one realized observation. What you see below are three scenarios with 20 observations each. With this representation, calculating default correlations between the securities becomes a trivial task as shown below in three cases. This way of representing default or survival is also correct as that represents the value of $1 of a security after the period under consideration. In other words, we can denote default by a 0, and survival by a 1. Let us look at how default correlations are calculated.ĭefault for any security is a binary event – the security either defaults, or it does not. Let us get the math out of the way first so we feel confident about the mechanics before going on to looking at an intuitive understanding. The question I am trying to address is something like this: when we say that the default correlation between A and B is 0.4, for example, what does it really mean? Does it mean that A and B will default together 40% of the time? Or does it mean that 40% of the defaults in either are “explained” by a default in the other? Or does it mean something completely different? Let us look at how default correlations are calculated, and then try to think about how to intuitively interpret a given default correlation number between two securities. To keep things simple, let us consider only two securities– A and B. Obviously the probabilities listed above do not include all the real of possibilities and that is why? What should I be weighing by? Thank you for your help.This is a brief article on default correlations – what it means, and how to interpret it. Hence the probability the firm survives year 1 is 98%, the firm surivevs to year 2 is (98%)^2, year 3 (98%)^3, survives to year 4 (98%)^4, survives year 5 (98%)^2 (.02)īut obviously these probability do not produce a pdf because they do not sum to 1. But what probability density should I use to weight the possible scenarios? I could assume that on any given year the probability Firm XYZ will default is 2%. The value of the bond should be the E(V), the expected value of all the possible payoffs. So here are all the possible scenarios for this bond $40 Default Yr1 Let say there is a risk this bond default and we estimate the recoveries on the bond are 40 cents on the dollar. Let say the coupons pay annually for simplicity and they pay out a 5% on a 100 par. So assume a bullet bond with a 5 year maturity. Given the current price of a bond and the current risk free rate, I am trying to calculate the probability of default. I am trying to build out a probability of default model for a bond. ![]()
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