Exact and Efficient Simulation of Correlated Defaults

Abstract

Abstract. Correlated default risk plays a significant role in financial markets. Dynamic intensity-based models, in which a firm default is governed by a stochastic intensity process, are widely used to model correlated default risk. The computations in these models can be performed by Monte Carlo simulation. The standard simulation method, which requires the discretization of the intensity process, leads to biased simulation estimators. The magnitude of the bias is often hard to quantify. This paper develops an exact simulation method for intensity-based models that leads to unbiased estimators of credit portfolio loss distributions, risk measures, and derivatives prices. In a first step, we construct a Markov chain that matches the marginal distribution of the point process describing the binary default state of each firm. This construction reduces the original estimation problem to one involving a Markov chain expectation. In a second step, we estimate the Markov chain expectation using a simple acceptance/rejection scheme that facilitates exact sampling. To address rare event situations, the acceptance/rejection scheme is embedded in an overarching selection/mutation scheme, in which a selection mechanism adaptively forces the chain into the regime of interest. Numerical experiments demonstrate the effectiveness of the method for a self-exciting model of correlated default risk.

Estimating Sensitivities of Portfolio Credit Risk Using Monte Carlo

“…For future work, we will study how to estimate sensitivities when the joint defaults are modeled using frailty models or self excited models, which are closely related to doubly stochastic models but are capable of capturing default clustering effects (see, for instance Giesecke et al 2010 for a thorough introduction of these models). In these models, the intensity function may not be continuous with respect to the parameter that we want to consider.…”

Multi-Name Extension to the Credit Grades and an Efficient Monte Carlo Method

“…In an effort to estimate the accurate probabilities within a reasonable computational time, we embed IPS to original standard Monte Carlo simulation algorithm. In the following two subsections, we provide a quick overview of the IPS inspired by the pioneering work Del Moral and Garnier [15] and subsequent papers Carmona, Forque and Vestal [14], Carmona and Crepey [16] and Giesecke et al [7].…”

“…Since the contagion effects heavily influence the correlations of defaults, capturing them in quantitative models is crucial. Existing dynamic credit risk models which deal with default contagion include, among others, Davis and Lo [1], Fan Yu [2], Frey and Backhaus [3], Frey and Runggaldier [4], Giesecke [5], Giesecke and Goldberg [6], Giesecke et al [7], Schönbucher [8], Takada and Sumita [9] and comprehensive surveys can be found in Chapter 9 of McNeil, Frey and Embrechts [10]. Generally, credit risk modeling methodologies are categorized to either reduced form approach or structural approach.…”

“…Generally, credit risk modeling methodologies are categorized to either reduced form approach or structural approach. In the reduced form approach, by introducing interacting intensities, default contagion can be captured by the jump up of the default intensity immediately after the default as in Davis and Lo [1], Fan Yu [2], Frey and Backhaus [3], Giesecke et al [7] and Takada and Sumita [9]. However, it is not easy to incorporate the mechanism where the crisis mode would resolve after some period.…”

Interacting particle systems for the computation of rare credit portfolio losses

“…Already several papers [3,8] appeared after the first version of this paper was first circulated. They show the strength of IPS-based Monte Carlo computations of small default probabilities, especially when other methods fail.…”