Estimating Tranche Spreads by Loss Process Simulation

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Estimating Tranche Spreads by Loss Process Simulation

by Kay Giesecke of Stanford University, and
Baeho Kim of Stanford University

July 15, 2007

Abstract: A credit derivative is a path dependent contingent claim on the aggregate loss in a portfolio of credit sensitive securities. We estimate the value of a credit derivative by Monte Carlo simulation of the affine point process that models the loss. We consider two algorithms that exploit the direct specification of the loss process in terms of an intensity. One algorithm is based on the simulation of intensity paths. Here discretization introduces bias into the results. The other algorithm facilitates exact simulation of default times and generates an unbiased estimator of the derivative price. We implement the algorithms to value index and tranche swaps, and we calibrate the loss process to quotes on the CDX North America High Yield index.

JEL Classification: C15, E47, G32.

Keywords: credit derivative, Monte Carlo simulation, Loss process, affine point process, time change, exact algorithm.

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