Importance sampling for stochastic simulations
Management Science
Bounded relative error in estimating transient measures of highly dependable non-Markovian systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Proceedings of the 35th conference on Winter simulation: driving innovation
Efficient importance sampling for reduced form models in credit risk
Proceedings of the 38th conference on Winter simulation
Fast Pricing of Basket Default Swaps
Operations Research
A Top-Down Approach to Multiname Credit
Operations Research
Exact Simulation of Point Processes with Stochastic Intensities
Operations Research
Affine Point Processes and Portfolio Credit Risk
SIAM Journal on Financial Mathematics
Exact Simulation of Point Processes with Stochastic Intensities
Operations Research
Monte Carlo Algorithms for Default Timing Problems
Management Science
Sequential Importance Sampling and Resampling for Dynamic Portfolio Credit Risk
Operations Research
Importance sampling for indicator markov chains
Proceedings of the Winter Simulation Conference
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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.