Exact and Efficient Simulation of Correlated Defaults

36 Pages Posted: 1 Nov 2009 Last revised: 1 Oct 2010

See all articles by Kay Giesecke

Kay Giesecke

Stanford University - Department of Management Science & Engineering

Hossein Kakavand

Stanford University

Mohammad Mousavi

Stanford University - Department of Management Science & Engineering

Hideyuki Takada

Toho University

Date Written: June 14, 2010

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.

Keywords: Correlated Default Risk, Portfolio Credit Risk, Intensity, Simulation, Variance Reduction, Intensity Model

Suggested Citation

Giesecke, Kay and Kakavand, Hossein and Mousavi, Mohammad and Takada, Hideyuki, Exact and Efficient Simulation of Correlated Defaults (June 14, 2010). Available at SSRN: https://ssrn.com/abstract=1497569 or http://dx.doi.org/10.2139/ssrn.1497569

Kay Giesecke (Contact Author)

Stanford University - Department of Management Science & Engineering ( email )

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HOME PAGE: http://https://giesecke.people.stanford.edu

Hossein Kakavand

Stanford University ( email )

Stanford, CA 94305
United States

Mohammad Mousavi

Stanford University - Department of Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Hideyuki Takada

Toho University ( email )

Room 4421
Miyama 2-2-1
Funabashi, Chiba 274-8510
Japan
(+81)-47-472-1856 (Phone)

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