## A Dynamic Correlation Modelling Framework with Consistent Recovery.” defaultrisk.com

Citations: | 5 - 2 self |

### BibTeX

@MISC{Li_adynamic,

author = {Yadong Li},

title = {A Dynamic Correlation Modelling Framework with Consistent Recovery.” defaultrisk.com},

year = {}

}

### OpenURL

### Abstract

This paper describes a flexible and tractable bottom-up dynamic correlation modelling framework with a consistent stochastic recovery specification. The stochastic recovery specification only models the first two moments of the spot recovery rate as the higher moments of the recovery rate have almost no contribution to the loss distribution and CDO tranche pricing. Observing that only the joint distribution of default indicators is needed to build the portfolio loss distribution, we argue that the default indicator copula should be used instead of the default time copula for the purpose of CDO tranche calibration and pricing. We then defined a generic class of default indicator copula with the “time locality ” property, which makes it easy to calibrate to index tranche prices across multiple maturities. This correlation modelling framework has the unique advantage that the joint distribution of default time and other dynamic properties of the model can be changed independently from the loss distribution and tranche prices. After calibrating the model to index tranche prices, existing top-down methods can be applied to the common factor process to construct very flexible systemic dynamics without changing the already calibrated tranche prices. This modelling framework therefore combines the best features of the bottom-up and top-down models: it is fully consistent with all the single name market information

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Citation Context ...ew information can be added by the realized loss and idiosyncratic factors. The exact pricing rather than a close lower bound can be obtained by a least-square Monte Carlo simulation as described in (=-=Longstaff & Schwartz 2001-=-). Both the realized loss and idiosyncratic dynamics can be tracked accurately within the Monte Carlo simulation. The Monte Carlo simulation is very useful for checking the accuracy of the lattice imp... |

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Citation Context ...ministic recovery often failed to calibrate to the index tranche market because it forces the senior most tranches to be risk free, leaving too much risk in the junior part of the capital structure. (=-=Andersen & Sidenius 2004-=-) first proposed the stochastic recovery for Gaussian Copula. More recently, a number of stochastic recovery specifications have been suggested for the base correlation framework, e.g. (Amraoui & Hiti... |

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Citation Context ...rom the index tranches because the spread dispersion, which is a critical factor in CDO pricing, is not captured by the top-down models. (Shonbucher, 2006), (Sidenius et al., 2006), (Bennani, 2005), (=-=Errais et al., 2009-=-) and (Arnsdorf & Halperin, 2007) are some representative examples of the top-down models. The bottom-up approach, on the other hand, starts with the single name spread dynamics and a correlation stru... |

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Citation Context ...sly. Due to these difficulties, there is no known bottom-up model that can produce good index tranche calibration and flexible spread dynamics to the best knowledge of the author. (Mortensen, 2006), (=-=Chapovsky et al., 2006-=-) and (Kogan, 2008) are some representative bottom-up dynamic correlation models. Under the current market conditions, the stochastic recovery is required for a bottom-up dynamic correlation model to ... |

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Citation Context ...ent static copula, which can produce the joint default time distribution in order to price default path-dependent instruments. Random Factor Loading (Andersen & Sidenius 2004) and the Implied Copula (=-=Hull & White 2006-=-) (Skarke 2005) are examples of the alternative static copulas. Another alternative modelling approach is to develop dynamic correlation models, which can price the spread-dependent correlation instru... |

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Citation Context ... 1τi<t and ri(0, t) are independent between names, it is well known that the portfolio loss distribution at time t can be approximated by a normal distribution according to the central limit theorem (=-=Shelton, 2004-=-). The normal approximation to the loss distribution is fully characterized by the mean and variance of the portfolio loss L(t), which can be computed as: n∑ n∑ n∑ E[L(t)] = E[ wili] = wiE[li] = wipi(... |

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