# Credit Risk Frontiers: Subprime Crisis, Pricing and Hedging, CVA, MBS, Ratings, and Liquidity

## Damiano Brigo

Language: English

Pages: 754

ISBN: 157660358X

Format: PDF / Kindle (mobi) / ePub

**A timely guide to understanding and implementing credit derivatives**

Credit derivatives are here to stay and will continue to play a role in finance in the future. But what will that role be? What issues and challenges should be addressed? And what lessons can be learned from the credit mess?

*Credit Risk Frontiers* offers answers to these and other questions by presenting the latest research in this field and addressing important issues exposed by the financial crisis. It covers this subject from a real world perspective, tackling issues such as liquidity, poor data, and credit spreads, as well as the latest innovations in portfolio products and hedging and risk management techniques.

- Provides a coherent presentation of recent advances in the theory and practice of credit derivatives
- Takes into account the new products and risk requirements of a post financial crisis world
- Contains information regarding various aspects of the credit derivative market as well as cutting edge research regarding those aspects

If you want to gain a better understanding of how credit derivatives can help your trading or investing endeavors, then *Credit Risk Frontiers* is a book you need to read.

The Independent (28 September 2015)

Trading the Fixed Income, Inflation and Credit Markets: A Relative Value Guide

∈ [0, 1]) where p x (t, T) = P(L(T) ≤ x |Ft ). It satisfies the following properties: (i) (ii) (iii) (iv) x → p x (t, T) is nondecreasing. p 1 (t, T) = 1. For each x ∈ [0, 1], T → p x (t, T) is nonincreasing. ( p x (t, T))t≥0 is a (Ft )-martingale. Except the last one, they reflect the fact that (L(t), t ≥ 0) is a nondecreasing process valued in [0, 1] and are thus arbitrage-free conditions. For t ≥ T, 1 L(T)≤x is both Gt and GT measurable, and from ∀X ∈ L 1 (Gt ), E[X |F] = E[X |Ft ] we deduce

2010 19:38 Printer Name: Yet to Come 100 Credit Derivatives: Methods Using equation (4.7) and the normalization condition M P[N(t + δt ) = M | N(t) = N] = 1 we can find the leading order in δt expressions for the transition elements P[N(t + δt ) = N | N(t) = N − 1] = P[N(t + δt ) = N | N(t) = N] = 1 − − 1, t) δt + O(δt2 ) 2 B (N, t) δt + O(δt ) B (N (4.71) (4.72) Inserting equations (4.71) and (4.72) into equation (4.70) and taking the limit δt → 0, we obtain equation (4.16). Appendix

availability of external ratings became a key component of regulation with Basel II, increasing furthermore the need for ratings. The irony is that the rating agencies’ worst failures relate to credit products that were, by design, built on credit ratings, such as collateralized debt obligations (CDOs) of mezzanine asset-backed securities (ABSs). In fact, the rating agencies have been hurt by the consequences of the weak parts of their business models: Who pays obviously makes a difference,

= (L n − K )+ ( L n naive − K )+ (5.63) are the heterogeneity correction factors (HCFs). Equation (5.62) decomposes the tranche expected loss into a weighted sum of loss contributions obtained with the naive top-down averaging over notionals of constituent names. The weights are given by the values of the product p n αn K . All the impact of heterogeneity of the portfolio is now hidden in HCF parameters (5.63). P1: OSO c05 JWBT388-Bielecki December 16, 2010 19:48 Printer Name: Yet to Come

equity tranche deltas are smaller when using the Markov chain. From a risk management perspective, an interesting feature is that the deltas with respect to underlying credit default swaps have the same order of magnitude in the different approaches. Let us first recall that, in the case of zero default-free interest rates, the default leg of a senior CDO tranche can be seen as a call option on a portfolio TABLE 6.2 Market and Model Deltas as in Arnsdorf and Halperin (2007) Tranches 0–3% 3–6%