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Bond Portfolio Investing and Risk Management by Vineer Bhansali

Bond Portfolio Investing and Risk Management by Vineer Bhansali

Author:Vineer Bhansali
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2011-09-14T16:00:00+00:00


The Market for Implied Correlation

In this section we will discuss implied correlation from the perspective of the Black-Scholes analogue for correlation products: the gaussian copula model. The gaussian copula model has more than a passing similarity with the simple Black-Scholes model for options and has suffered its shares of attacks. However, just like its older cousin, the Black-Scholes model, the gaussian copula not only has survived but also has thrived. The reasons are multifold: (1) No one who trades correlation products really believes that the gaussian copula model is the last word, but by their usage, they all agree that it is an excellent starting point and relatively easy to conceptualize (no one believes that Black-Scholes for options is the last word either, but the formula, by virtue of its clarity and simplicity, has survived 30 years in great style); (2) exact solutions are easy to obtain for products such as tranches under reasonable assumptions, and when exact solutions are not available, the framework allows for straightforward numerical simulations; and (3) it is easy to communicate the value of the variables and parameters although the meaning of these parameters is not always transparent. However, we should hasten to add that much research has continued to expand the simple copula model to make more realistic assumptions. A thorough review of this exciting field is beyond the scope of this book. Tranche markets are not limited to investment-grade indices. There are also tranches on the high-yield indices that are reasonably liquid as of this writing, as well as tranches on indices of subprime mortgage issuers (ABX and TABX). Discussion of the subprime tranche market would require us to delve into mortgage credit and prepayment models, so in this discussion we will focus mainly on pure credit tranches.

Let us review how correlation enters the pricing of tranches. As discussed earlier, a tranche is a spread on the losses of the underlying index. A tranche is defined by an attachment point (lower strike Kd) and a detachment point (upper strike Ku). If the loss on the underlying index is Li(t), then the tranche loss is simply



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