Pricing CDOs with State Dependent Stochastic Recovery Rates

Abstract

Up to the 2007 crisis, research within bottom-up CDO models mainly concentrated on the dependence between defaults. However, due to the substantial increase in the market price of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we focus first on deterministic recovery rates in a factor copula framework. We use stochastic orders theory to assess the impact of a recovery markdown on CDOs and show that it leads to an increase of the expected loss on senior tranches, even though the expected loss on the portfolio is kept fixed. This result applies to a wide range of latent factor models. We then suggest introducing stochastic recovery rates in such a way that the conditional on the factor expected loss (or equivalently the large portfolio approximation) is the same as in the recovery markdown case. However, granular portfolios behave differently. We show that a markdown is associated with riskier portfolios that when using the stochastic recovery rate framework. As a consequence, the expected loss on a senior tranche is larger in the former case, whatever the attachment point. We also deal with implementation and numerical issues related to the pricing of CDOs within the stochastic recovery rate framework. Due to differences across names regarding the conditional (on the factor) losses given default, the standard recursion approach becomes problematic. We suggest approximating the conditional on the factor loss distributions, through expansions around some base distribution. Finally, we show that the independence and comonotonic cases provide some easy to compute bounds on expected losses of senior or equity tranches.

A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance

“…We set q = 1 52 , say, on a weekly basis, and simulate the risk-neutralized interest rate process per Equation (8) ln c index,j , knowing that ln c j and ln c index,j are normal random variables and the coefficient of correlation between them is ρ c . After simulating these processes, PV R,0 can be easily calculated via averaging over the contingent payoffs corresponding to the simulated values.…”

Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

“…This has led to adding stochastic recovery to CDO models (c.f. [8][9][10][11][12][13]), which is now standard practice in industry.…”

“…This has led to adding stochastic recovery to CDO models (c.f. [8][9][10][11][12][13]), which is now standard practice in industry.However, stochastic recovery has not yet received equally widespread interest and acceptance for other credit products such as defaultable bonds, credit default swaps and credit linked notes. In fact, there are a dearth of pricing formulas for credit products where recovery is modeled explicitly.…”

The Limits of Granularity Adjustments

“…For convenience, we have calculated GA1 only (usual granularity adjustments) in this model. Note that there are a lot of different ways of introducing recovery risk in such credit risk models: see Pykhtin (2003), Chen and Joslin (2012), Amraoui et al (2012), among others. Our specification has been chosen for the sake of simplicity only.…”