April 14th, 2005, 11:40 am
If you have all the single name spreads, you know the spread of the basket, but not of tranches on the basket. To compute the price of tranches, you need to know the entire joint distribution of prices of the underlyings.Instead of that, you can make the highly simplified assumption that all pairwise correlations are the same and there are no higher order effects. The market convention is to use the Gaussian copula time to default correlation. If you do that, you can plug in a value for correlation and get a price for any tranche. Or you can plug in the price of any tranche and solve for the correlation that implies it (subject to the unpleasantness that you will sometimes get multiple or no solutions, which is one big reason people use base correlations instead).Therefore, as long as the relation between implied correlations and tranche prices is one-to-one, prices and correlations are equivalent ways to express the same thing, like Farenheit and Celsius temperature. You can convert from one to the other easily. You will get a different implied correlation for each tranche, and different correlations for the same tranche in different baskets.