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    Efficient randomized quasi-Monte Carlo methods for portfolio market risk
    (Elsevier, 2017) Sak, Halis; Başoğlu, İsmail
    We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no paper discussing combining the randomized quasi-Monte Carlo method with variance reduction techniques. In this paper, we combine the randomized quasi-Monte Carlo method with importance sampling and stratified importance sampling. Numerical results for realistic portfolio examples suggest that replacing pseudorandom numbers (Monte Carlo) with quasi-random sequences (quasi-Monte Carlo) in the simulations increases the robustness of the estimates once we reduce the effective dimension and the impact of the non-smoothness of the integrands. (C) 2017 Elsevier B.V. All rights reserved.
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    Öğe
    Efficient simulations for a bernoulli mixture model of portfolio credit risk
    (Springer, 2018) Başoğlu, İsmail; Hormann, Wolfgang; Sak, Halis
    We consider the problem of calculating tail loss probability and conditional excess for the Bernoulli mixture model of credit risk. This is an important problem as all credit risk models proposed in literature can be represented as Bernoulli mixture models. Thus, we deviate from the efficient simulation of credit risk literature in that we propose an efficient simulation algorithm for this general Bernoulli mixture model in contrast to previous works that focus on specific credit risk models like CreditRisk or Credit Metrics. The algorithm we propose is a combination of stratification, importance sampling based on cross-entropy, and inner replications using the geometric shortcut method. We evaluate the efficiency of our general method considering three different examples: CreditRisk and two of the latent variable models, the Gaussian and the t-copula model. Numerical results suggest that the proposed general algorithm is more efficient than the benchmark methods for these specific models.